Que 1: in women who suffer from migraine …………………. are classified menstrual migraines, which tend to be more severe and longer lasting . a) 5% – 10% b) 45% – 55% c) 20% – 50% d) 65%-75% Que 2: why are the women on average, slightly shorter than men a) They have fat then man which contributes to stature b) Their long bones are sealed and stop growing earlier than men c) Their brains are somewhat smaller than man’s brain d) Their brains are somewhat larger than man, brain que 3: menopause frequently occurs between ………………..age of year a) 25-30 b) 45-55 c) 35-40 d) 65-75 que 4: this hormone causes enlargement of the larynx and an increase in the length and thickness of the vocal cords. A) estrogen 2) cholesterol 3) progesterone 4) testosterone Que 5: the reproductive cycle includes which of the following interconnected sets of events a) Ovarian cycle b) Urinary cycle c) Placental cycle d) Female prostate cycle Que 6: high level of circulating progesterone have been associated with : a) Excessive milk production b) Ovarian cancer c) Inability to breast feed a new born child d) Pregnancy Que 7: although variations exist, ovulation typically occurs on the …………day before mensuaration a) 1st b) 14th c) 7th d) 28th Que 8: LH stimulates interstitial cells a) To decrease GnRH b) To produce FSH c) To produce testosterones d) To produce sperm Que 9:what region of the uterus is shed during menstration? a) Stratum basalis of the myometrium b) Stratum basalis of the endometrium c) Stratum functionalis of the endometrium d) Perimetrium Que 10: the phenomenon is which women living in close proximity tend to menstruate at approximately the time is called. a) Precocious puberty b) Menstrual synchrony’ c) Delayed puberty d) Ovarian synchrony Que 11.studies have shown that healthy menstruating women a) Should not participate in sports b) Often feel ill or weak when exercising c) Are able to safety engage in athletic activities d) Can contaminate others and should not engage in contacts sports. Que 12: which term below describes a chemical that resembles steroid hormones and posses threat to maintain homeostasis. a) Androgens b) Prostaglandins c) Endocrine disruptors d) All of the above Que 13: one of the primary function of ……….is preparing and sustaining the uterus of pregnancy a) Testosterone b) Progesterone c) Estradiol d) inhibin Que 14: typically ovulation occurs a) at the end of the uterine phase b) at the start of follicular phase c) during an increase of LH in the ovarian cycle d) at the middle of the luteal phase

Que 1: in women who suffer from migraine …………………. are classified menstrual migraines, which tend to be more severe and longer lasting . a) 5% – 10% b) 45% – 55% c) 20% – 50% d) 65%-75% Que 2: why are the women on average, slightly shorter than men a) They have fat then man which contributes to stature b) Their long bones are sealed and stop growing earlier than men c) Their brains are somewhat smaller than man’s brain d) Their brains are somewhat larger than man, brain que 3: menopause frequently occurs between ………………..age of year a) 25-30 b) 45-55 c) 35-40 d) 65-75 que 4: this hormone causes enlargement of the larynx and an increase in the length and thickness of the vocal cords. A) estrogen 2) cholesterol 3) progesterone 4) testosterone Que 5: the reproductive cycle includes which of the following interconnected sets of events a) Ovarian cycle b) Urinary cycle c) Placental cycle d) Female prostate cycle Que 6: high level of circulating progesterone have been associated with : a) Excessive milk production b) Ovarian cancer c) Inability to breast feed a new born child d) Pregnancy Que 7: although variations exist, ovulation typically occurs on the …………day before mensuaration a) 1st b) 14th c) 7th d) 28th Que 8: LH stimulates interstitial cells a) To decrease GnRH b) To produce FSH c) To produce testosterones d) To produce sperm Que 9:what region of the uterus is shed during menstration? a) Stratum basalis of the myometrium b) Stratum basalis of the endometrium c) Stratum functionalis of the endometrium d) Perimetrium Que 10: the phenomenon is which women living in close proximity tend to menstruate at approximately the time is called. a) Precocious puberty b) Menstrual synchrony’ c) Delayed puberty d) Ovarian synchrony Que 11.studies have shown that healthy menstruating women a) Should not participate in sports b) Often feel ill or weak when exercising c) Are able to safety engage in athletic activities d) Can contaminate others and should not engage in contacts sports. Que 12: which term below describes a chemical that resembles steroid hormones and posses threat to maintain homeostasis. a) Androgens b) Prostaglandins c) Endocrine disruptors d) All of the above Que 13: one of the primary function of ……….is preparing and sustaining the uterus of pregnancy a) Testosterone b) Progesterone c) Estradiol d) inhibin Que 14: typically ovulation occurs a) at the end of the uterine phase b) at the start of follicular phase c) during an increase of LH in the ovarian cycle d) at the middle of the luteal phase

This assignment challenges you to analyze how two writers present arguments about a significant issue or topic. For this assignment, you will choose two current newspaper or scholarly journal articles that focus on a current issue relevant to the people on the continent of Africa, and/or people of African descent. Your goal is to identify the purposes and claims of each author, locate their arguments in a rhetorical situation, and analyze the appeals each writer makes to support their argument. You will then evaluate the arguments: which author better satisfies their readers? Which author crafts the more fitting response? In sum, then, the main goals are: 1. Identify the purposes and claims that two authors make about a significant issue. 2. Locate the arguments in a rhetorical situation (what exigencies do the authors address? What constraints and resources exist for the authors? To whom are they writing? When and where was each article published? 3. Analyze the appeals (logical, ethical, emotional) put forth by the writers. 4. Evaluate the arguments. Which argument is more fitting? Which author better satisfies readers? (Your evaluation need not be either/or: maybe one author is more effective logically, for instance, while the second author is more effective ethically and emotionally.)

This assignment challenges you to analyze how two writers present arguments about a significant issue or topic. For this assignment, you will choose two current newspaper or scholarly journal articles that focus on a current issue relevant to the people on the continent of Africa, and/or people of African descent. Your goal is to identify the purposes and claims of each author, locate their arguments in a rhetorical situation, and analyze the appeals each writer makes to support their argument. You will then evaluate the arguments: which author better satisfies their readers? Which author crafts the more fitting response? In sum, then, the main goals are: 1. Identify the purposes and claims that two authors make about a significant issue. 2. Locate the arguments in a rhetorical situation (what exigencies do the authors address? What constraints and resources exist for the authors? To whom are they writing? When and where was each article published? 3. Analyze the appeals (logical, ethical, emotional) put forth by the writers. 4. Evaluate the arguments. Which argument is more fitting? Which author better satisfies readers? (Your evaluation need not be either/or: maybe one author is more effective logically, for instance, while the second author is more effective ethically and emotionally.)

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What is the prime purpose of selecting a composite material over material from the other family groups? MODULE 3 – STRUCTURE OF SOLID MATERIALS The ability of a material to exist in different space lattices is called a. Allotropic b. Crystalline c. Solvent d. Amorphous Amorphous metals develop their microstructure as a result of ___________. a. Dendrites b. Directional solidification c. Slip d. Extremely rapid cooling In an alloy, the material that dissolves the alloying element is the ___________. a. Solute b. Solvent c. Matrix d. Allotrope What is the coordination number (CN) for the fcc structure formed by ions of sodium and chlorine that is in the chemical compound NaCl (salt) ? a. 6 b. 8 c. 14 d. 16 What pressure is normally used in constructing a phase diagram? a. 100 psi b. Depends on material c. Ambient d. Normal atmospheric pressure What line on a binary diagram indicates the upper limit of the solid solution phase? a. Liquidus b. Eutectic c. Eutectoid d. Solidus What holds the atoms (ions) together in a compound such as NaCl are electrostatic forces between ___________. a. Atom and ion b. Covalent bonds c. Electrons and nuclei d. Neutrons Diffusion of atoms through a solid takes place by two main mechanisms. One is diffusion through vacancies in the atomic structure. Another method of diffusion is ___________. a. Cold b. APF c. Substitutional d. Interstitial Give a brief explanation of the Lever rule (P117) Grain boundaries ___________ movement of dislocations through a solid. a. Improve b. Inhibit c. Do not affect Iron can be alloyed with carbon because it is ___________. a. Crystalline b. Amorphous c. A mixture d. Allotropic Metals can be cooled only to crystalline solids. a. T (true) b. F (false) Sketch an fcc unit cell. Metals are classified as crystalline materials. Name one metal that is an amorphous solid and name at least one recent application in which its use is saving energy or providing greater strength and/or corrosion resistance. MODULE 4 – MECHANICAL PROPERTIES Give two examples of a mechanical property. a. Thermal resistance b. Wear resistance c. Hardness d. Strength Scissors used in the home cut material by concentrating forces that ultimately produce a certain type of stress within the material. Identify this stress. a. Bearing stress b. Shearing stress c. Compressive stress An aluminum rod 1 in. in diameter (E =10.4 x 106psi) experiences an elastic tensile strain of 0.0048 in./in. Calculate the stress in the rod. a. 49,920 ksi b. 49,920 psi c. 49,920 msi A 1-in.-diameter steel circular rod is subject to a tensile load that reduces its cross-sectional area to 0.64 in2. Express the rod’s ductility using a standard unit of measure. a. 18.5% b. 1.85% c. 18.5 d. (a) and (c) What term is used to describe the low-temperature creep of polymerics? a. Springback b. Creep rupture c. Cold flow d. Creep forming MODULE 7 – TESTING, FAILURE ANALYSIS, STANDARDS, & INSPECTION Factors of safety are defined either in terms of the ultimate strength of a material or its yield strength. In other words, by the use of a suitable factor, the ultimate or yield strength is reduced in size to what is known as the design stress or safe working stress. Which factor of safety would be more appropriate for a material that will be subjected to repetitious, suddenly applied loads? Product liability court cases have risen sharply in recent years because of poor procedures in selecting materials for particular applications. Assuming that a knowledge of a material’s properties is a valid step in the selection process, cite two examples where such lack of knowledge could or did lead to failure or unsatisfactory performance. Make a sketch and fully dimension an Izod impact test specimen. Which agency publishes the Annual Book of standard test methods used worldwide for evaluation of materials? a. NASA b. NIST c. ASTM d. SPE

What is the prime purpose of selecting a composite material over material from the other family groups? MODULE 3 – STRUCTURE OF SOLID MATERIALS The ability of a material to exist in different space lattices is called a. Allotropic b. Crystalline c. Solvent d. Amorphous Amorphous metals develop their microstructure as a result of ___________. a. Dendrites b. Directional solidification c. Slip d. Extremely rapid cooling In an alloy, the material that dissolves the alloying element is the ___________. a. Solute b. Solvent c. Matrix d. Allotrope What is the coordination number (CN) for the fcc structure formed by ions of sodium and chlorine that is in the chemical compound NaCl (salt) ? a. 6 b. 8 c. 14 d. 16 What pressure is normally used in constructing a phase diagram? a. 100 psi b. Depends on material c. Ambient d. Normal atmospheric pressure What line on a binary diagram indicates the upper limit of the solid solution phase? a. Liquidus b. Eutectic c. Eutectoid d. Solidus What holds the atoms (ions) together in a compound such as NaCl are electrostatic forces between ___________. a. Atom and ion b. Covalent bonds c. Electrons and nuclei d. Neutrons Diffusion of atoms through a solid takes place by two main mechanisms. One is diffusion through vacancies in the atomic structure. Another method of diffusion is ___________. a. Cold b. APF c. Substitutional d. Interstitial Give a brief explanation of the Lever rule (P117) Grain boundaries ___________ movement of dislocations through a solid. a. Improve b. Inhibit c. Do not affect Iron can be alloyed with carbon because it is ___________. a. Crystalline b. Amorphous c. A mixture d. Allotropic Metals can be cooled only to crystalline solids. a. T (true) b. F (false) Sketch an fcc unit cell. Metals are classified as crystalline materials. Name one metal that is an amorphous solid and name at least one recent application in which its use is saving energy or providing greater strength and/or corrosion resistance. MODULE 4 – MECHANICAL PROPERTIES Give two examples of a mechanical property. a. Thermal resistance b. Wear resistance c. Hardness d. Strength Scissors used in the home cut material by concentrating forces that ultimately produce a certain type of stress within the material. Identify this stress. a. Bearing stress b. Shearing stress c. Compressive stress An aluminum rod 1 in. in diameter (E =10.4 x 106psi) experiences an elastic tensile strain of 0.0048 in./in. Calculate the stress in the rod. a. 49,920 ksi b. 49,920 psi c. 49,920 msi A 1-in.-diameter steel circular rod is subject to a tensile load that reduces its cross-sectional area to 0.64 in2. Express the rod’s ductility using a standard unit of measure. a. 18.5% b. 1.85% c. 18.5 d. (a) and (c) What term is used to describe the low-temperature creep of polymerics? a. Springback b. Creep rupture c. Cold flow d. Creep forming MODULE 7 – TESTING, FAILURE ANALYSIS, STANDARDS, & INSPECTION Factors of safety are defined either in terms of the ultimate strength of a material or its yield strength. In other words, by the use of a suitable factor, the ultimate or yield strength is reduced in size to what is known as the design stress or safe working stress. Which factor of safety would be more appropriate for a material that will be subjected to repetitious, suddenly applied loads? Product liability court cases have risen sharply in recent years because of poor procedures in selecting materials for particular applications. Assuming that a knowledge of a material’s properties is a valid step in the selection process, cite two examples where such lack of knowledge could or did lead to failure or unsatisfactory performance. Make a sketch and fully dimension an Izod impact test specimen. Which agency publishes the Annual Book of standard test methods used worldwide for evaluation of materials? a. NASA b. NIST c. ASTM d. SPE

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• Question 1 10 out of 10 points “Fortune lifts and Fortune fells the lucky and unlucky every day. No prophet on earch can tell a man his fate.” • Question 2 10 out of 10 points “Tell me the news again whatever it is . . . . sorrow and I are hardly strangers. I can bear the worse.” • Question 3 10 out of 10 points “Creon shows the world that of all the ills afflicting men the worst is lack of judgment.” • Question 4 10 out of 10 points “Too late, too late, you see what justice means.” • Question 5 10 out of 10 points “Take me away, quickly, out of sight. I don’t exist — I’m no one. Nothing.” • Question 6 10 out of 10 points “That will come when it comes; we must deal with all that lies before us. The future rests with the ones who tend the future.” • Question 7 10 out of 10 points “The mighty words of the proud are paid in full with mighty blows of fate, and at long last those blows will teach us wisdom.” • Question 8 10 out of 10 points “Whatever I touch goes wrong — once more a crushing fate’s come down upon my head.” • Question 9 10 out of 10 points “Believe me, when a man has squandered his true joys, he’s good as dead, I tell you, a living corpse.” • Question 10 10 out of 10 points “What should I do? Tell me . . . I’ll obey

• Question 1 10 out of 10 points “Fortune lifts and Fortune fells the lucky and unlucky every day. No prophet on earch can tell a man his fate.” • Question 2 10 out of 10 points “Tell me the news again whatever it is . . . . sorrow and I are hardly strangers. I can bear the worse.” • Question 3 10 out of 10 points “Creon shows the world that of all the ills afflicting men the worst is lack of judgment.” • Question 4 10 out of 10 points “Too late, too late, you see what justice means.” • Question 5 10 out of 10 points “Take me away, quickly, out of sight. I don’t exist — I’m no one. Nothing.” • Question 6 10 out of 10 points “That will come when it comes; we must deal with all that lies before us. The future rests with the ones who tend the future.” • Question 7 10 out of 10 points “The mighty words of the proud are paid in full with mighty blows of fate, and at long last those blows will teach us wisdom.” • Question 8 10 out of 10 points “Whatever I touch goes wrong — once more a crushing fate’s come down upon my head.” • Question 9 10 out of 10 points “Believe me, when a man has squandered his true joys, he’s good as dead, I tell you, a living corpse.” • Question 10 10 out of 10 points “What should I do? Tell me . . . I’ll obey

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6. The primary operating goal of a publicly-owned firm trying to best serve its stockholders should be to a. Maximize managers’ own interests, which are by definition consistent with maximizing shareholders’ wealth. b. Maximize the firm’s expected EPS, which must also maximize the firm’s price per share. c. Minimize the firm’s risks because most stockholders dislike risk. In turn, this will maximize the firm’s stock price. d. Use a well-structured managerial compensation package to reduce conflicts that may exist between stockholders and managers. e. Since it is impossible to measure a stock’s intrinsic value, the text states that it is better for managers to attempt to maximize the current stock price than its intrinsic value.

6. The primary operating goal of a publicly-owned firm trying to best serve its stockholders should be to a. Maximize managers’ own interests, which are by definition consistent with maximizing shareholders’ wealth. b. Maximize the firm’s expected EPS, which must also maximize the firm’s price per share. c. Minimize the firm’s risks because most stockholders dislike risk. In turn, this will maximize the firm’s stock price. d. Use a well-structured managerial compensation package to reduce conflicts that may exist between stockholders and managers. e. Since it is impossible to measure a stock’s intrinsic value, the text states that it is better for managers to attempt to maximize the current stock price than its intrinsic value.

Answer: d
WEEKLY ASSIGNMENT #2 YOU 1. Verify for the Cobb-Douglas production function P(L;K) = 1:01L:75K:25 that the production will be doubled if both the amount of labor and the amount of capital are doubled. How much must you increase capital K to double production? How much must you increase labor by to double production? 1 2. Let F(x; y) = 1+ p 4 ? y2. Evaluate F(3; 1). Find and sketch the domain of F. Find the range of F. 2 3. Draw a contour map of the function showing several level curves. (a) g(x; y) = x2 ? y2 (b) s(x; y) = y=(x2 + y2) 3 4. Find the limit if it exists or show that the limit does not exist. You do not have to use the epsilon delta method so it will either be “obviously” continuous or you will have to show that it is not by finding two paths which give different results. (a) lim (x;y)!(2;?1) x2y + xy2 x2 ? y2 (b) lim (x;y)!(0;0) x4 ? 4y2 x2 + 2y2 (c) lim (x;y)!(0;0) xy p x2 + y2 4 5. The temperature T at a location in the Norther Hemisphere depends on the longitude x, the latitude y, and the time t. What are the meaning of the partial derivatives @T=@t; @T=@x; @T=@y? Moscow lies at 46:73N; 117W. Suppose that at 9 am on January 1st the wind is blowing hot air to the northeast so the air to the west and south is warm, and the air to the north and east is cooler. Would you expect fx(117; 4673; 9); fy(117; 4673; 9); ft(117; 4673; 9) to be positive negative or positive? 5 6. Find the first partial derivatives of the following functions. (a) f(x; y) = x4 + 5xy3 (b) g(x; y) = t2e?t (c) h(s; t) = ln(s + t2) (d) i(x; y) = x y (e) R(p; q) = arctan pq2 6 7. Find @z=@x and @z=@y for the following, assuming that f and g are differentiable single variable functions Hint: Your answer should use f0 and/or g0. z = f(x)g(y) ; z = f(x=y) 7

WEEKLY ASSIGNMENT #2 YOU 1. Verify for the Cobb-Douglas production function P(L;K) = 1:01L:75K:25 that the production will be doubled if both the amount of labor and the amount of capital are doubled. How much must you increase capital K to double production? How much must you increase labor by to double production? 1 2. Let F(x; y) = 1+ p 4 ? y2. Evaluate F(3; 1). Find and sketch the domain of F. Find the range of F. 2 3. Draw a contour map of the function showing several level curves. (a) g(x; y) = x2 ? y2 (b) s(x; y) = y=(x2 + y2) 3 4. Find the limit if it exists or show that the limit does not exist. You do not have to use the epsilon delta method so it will either be “obviously” continuous or you will have to show that it is not by finding two paths which give different results. (a) lim (x;y)!(2;?1) x2y + xy2 x2 ? y2 (b) lim (x;y)!(0;0) x4 ? 4y2 x2 + 2y2 (c) lim (x;y)!(0;0) xy p x2 + y2 4 5. The temperature T at a location in the Norther Hemisphere depends on the longitude x, the latitude y, and the time t. What are the meaning of the partial derivatives @T=@t; @T=@x; @T=@y? Moscow lies at 46:73N; 117W. Suppose that at 9 am on January 1st the wind is blowing hot air to the northeast so the air to the west and south is warm, and the air to the north and east is cooler. Would you expect fx(117; 4673; 9); fy(117; 4673; 9); ft(117; 4673; 9) to be positive negative or positive? 5 6. Find the first partial derivatives of the following functions. (a) f(x; y) = x4 + 5xy3 (b) g(x; y) = t2e?t (c) h(s; t) = ln(s + t2) (d) i(x; y) = x y (e) R(p; q) = arctan pq2 6 7. Find @z=@x and @z=@y for the following, assuming that f and g are differentiable single variable functions Hint: Your answer should use f0 and/or g0. z = f(x)g(y) ; z = f(x=y) 7

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Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

Homework #8  Consider the veracity or falsehood of each of the following statements. For bonus, argue for those that you believe are true while providing a counterexample for those that you believe are false.  If the first and third rows of A are equal, then det A 0.  If P is a projection, then uCP if and only if Pu  u.  If P is a projection, and detP  0, then P  I .  If A has determinant 10, then 1 A has determinant 1 10 .  If B is invertible, 1 1 det(A B ) det A (detB) .  If P is a projection, and R  2P I , then 2 R  I .  If P is a projection, and P  I , then detP  0 .  Short Computations. All of the following do not involve long computations:  Suppose 1 2 1 5 1 8 A                  and 1 9 2 4 3 1 A                   . Compute 7 13 19 A         .  Compute               0 8 7 1 0 2 3 4 5 3 0 9 2 0 0 0 3 0 0 0 1 9 3 2 0 det .  Use Cramer’s Rule to find 5 x (hint: you do not need your calculator). 1 2 3 4 5 5x 2x 8x x 3x 13 1 3 3x 5x 0 1 3 5 3x 3x 3x 9 1 2 3 5 3x 2x x 2x 7 1 3 x 4x 0 Let A 1 2 3 4 1 3 4 6 2 5 13 15 4 10 15 31 . Given is that det A  61. Do the following:  1 1 2 4 2 3 5 10 3 4 13 15 4 6 15 31 det  det2A  1 3 4 6 2 4 6 8 2 5 13 15 4 10 15 31 det  1 3 4 6 2 5 13 15 4 10 15 31 1 2 3 4 det  Consider the matrix A  0 1 0 0 0 0 1 0 0 0 0 1 1 2 2 1           . Use row (or column) expansion to compute det(xI A) .  The matrix 4 1 1 2 1 1 1 4 1 1 2 1 1 1 4 1 1 2 2 1 1 4 1 1 1 2 1 1 4 1 1 1 2 1 1 4 1 6 P is the projection matrix for the column space of matrix A. This matrix A is also known to be of full rank. Answer the following, giving reasons for your answers.  Find a transparent basis and the dimension for the column space of P.  Find a basis and the dimension for the column space of A .  What size is the matrix A ?  Find a transparent basis and the dimension for the null space of P.  Find a transparent basis and the dimension for the row space of P.  Find a basis and the dimension for the null space of A.  For which of the following b can you find a solution to the system Ax b ? This does not mean you should find a solution, only whether one could or not. 10 17 19 14 10 17 19 14 13 10 17 19 14 13 23 1 1 1 1 1 1 .  It is known that certain vector u is a solution to the system Ax c . Give all solutions to Ax c .  It is also known that 1 2 3 4 5 6 Ax does not have a solution. How would you change the constant vector so that there would be a solution? Extra Problems.  Fill in the blank with the best possible expression to complete the sentence truthfully. Only that one will be counted correct. 1. matrix with two equal columns will have zero determinant. 1 2 3 Some Every No 2. If A is invertible, then A commute with its inverse. 1 2 3 must always can will not 3. If A is 6  9 , then the columns of A be linearly independent. While in AT , the columns be linearly independent. 1 2 3 can have to cannot 4. Let A be square, and suppose Ax  0 has a nontrivial solution. Then detA equal 0. 1 2 3 may cannot must 5. Let A and B be 3 3. Then det (AB) equal det(A)det(B) . 1 2 3 could must couldn’t 6. Let A be square and suppose detA  0. Then have an inverse 1 2 3 will not may must always 7. Let A and B be 2  2 . Then det (A B) equal det(A)  det(B) . 1 2 3 could must could not 8. exist a 6  6 matrix all of whose entries are whole numbers and its determinant is 2 5 . 1 2 3 There does There does not There might Bonus: Consider the matrix 0 0 1 0 2 0 n 0 . Give its determinant as a function of n.

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WEEKLY ASSIGNMENT #5.5/EXAM REVIEW YOU 1. True/False Answers Probably want to think about them before you read the answers: (a) fy(a; b) = limh!b f(a;y)?f(a;b) y?b is True (b) There exists a function f with continuous second-order partial derivatives such that fx(x; y) = x + y2 and fy(x; y) = x ? y2. This is False. (c) fxy = @2f @x@y . This is False, because order of differentiation matters (d) Dkf(x; y; z) = fz(x; y; z). This is True. (e) If f(x; y) ! L as (x; y) ! (a; b) along every strait line through (a; b), then lim(x;y)!(a;b) f(x; y) = L. This is False, because there could be a non-strait path that gives a different answer. (f) If fx(a; b) and fy(a; b) both exist, the f is differentiable at (a; b). This is False, read theorem 8 in 14.4 (g) If f has a local minimum at (a; b) and f is differentiable at (a; b), then rf(a; b) = 0. This is True. (h) If f(x; y) = ln y, then rf(x; y) = 1=y. This is false, since gradient of f is a vector function. (i) If f is a function, then lim (x;y)!(2;5) f(x; y) = f(2; 5): This is false, since f may not be continuous. (j) If (2; 1) is a critical point of f and fxx(2; 1)fyy(2; 1) < fxy(2; 1)2 then f has a saddle point at (2; 1). This is True (k) if f(x; y) = sin x + sin y then ? p 2  Duf(x; y)  p 2: This is True since the gradient vector will always have length less than p 2. (l) If f(x; y) has two local maxima, then f must have a local minimum. This is False. It is true for single variable continuous functions, but even if the f(x; y) is continuous this is still not true. Think a bit about why and consider the example (x2 ? 1)2 ? (x2  y ? x ? 1)2. From the review section of chapter 14 (question and answers attached) Do as many as you have time for and pay particular attention to the following : 8-11, 13-17, 25, 27, 29, 31, 33, 35-37, 43-47, 51-56, 59-63. These bolded ones haven’t been collected on any homework, so make sure you can do these especially. I know that is a lot to study and I’m not expecting most people to do them all, but do a bunch and you should be good. 1 Questions from the exam will include true false, only from the above problems. The rest of the questions will come directly (or with minor changes) from the homework and from the review questions listed above from the chapter 14 review. 2

WEEKLY ASSIGNMENT #5.5/EXAM REVIEW YOU 1. True/False Answers Probably want to think about them before you read the answers: (a) fy(a; b) = limh!b f(a;y)?f(a;b) y?b is True (b) There exists a function f with continuous second-order partial derivatives such that fx(x; y) = x + y2 and fy(x; y) = x ? y2. This is False. (c) fxy = @2f @x@y . This is False, because order of differentiation matters (d) Dkf(x; y; z) = fz(x; y; z). This is True. (e) If f(x; y) ! L as (x; y) ! (a; b) along every strait line through (a; b), then lim(x;y)!(a;b) f(x; y) = L. This is False, because there could be a non-strait path that gives a different answer. (f) If fx(a; b) and fy(a; b) both exist, the f is differentiable at (a; b). This is False, read theorem 8 in 14.4 (g) If f has a local minimum at (a; b) and f is differentiable at (a; b), then rf(a; b) = 0. This is True. (h) If f(x; y) = ln y, then rf(x; y) = 1=y. This is false, since gradient of f is a vector function. (i) If f is a function, then lim (x;y)!(2;5) f(x; y) = f(2; 5): This is false, since f may not be continuous. (j) If (2; 1) is a critical point of f and fxx(2; 1)fyy(2; 1) < fxy(2; 1)2 then f has a saddle point at (2; 1). This is True (k) if f(x; y) = sin x + sin y then ? p 2  Duf(x; y)  p 2: This is True since the gradient vector will always have length less than p 2. (l) If f(x; y) has two local maxima, then f must have a local minimum. This is False. It is true for single variable continuous functions, but even if the f(x; y) is continuous this is still not true. Think a bit about why and consider the example (x2 ? 1)2 ? (x2  y ? x ? 1)2. From the review section of chapter 14 (question and answers attached) Do as many as you have time for and pay particular attention to the following : 8-11, 13-17, 25, 27, 29, 31, 33, 35-37, 43-47, 51-56, 59-63. These bolded ones haven’t been collected on any homework, so make sure you can do these especially. I know that is a lot to study and I’m not expecting most people to do them all, but do a bunch and you should be good. 1 Questions from the exam will include true false, only from the above problems. The rest of the questions will come directly (or with minor changes) from the homework and from the review questions listed above from the chapter 14 review. 2

1 Hankerson Project Three: Culture and the African American Experience The Media Analysis This project will help you: ?develop your analytical skills. ?expand your understanding of media and how it operates. Background: For this project, we will examine select media representations of the African American culture. These media representations will further our understanding of how media portrayals–specifically African American media portrayals–operate. Ultimately, we will use this knowledge to engage with the overall task for this project which asks us to write a media analysis about a cultural media portrayal of interest. Task: As a frame for this project, we will draw from Afrobella’s DzAn Open Letter to Hip Hopdz which explores Afrobella’s perceptions of the state of hip hop. Your task for this project will be to compose a media analysis about Afrobella’s DzAn Open Letter to Hip Hop.dz Alternatively, you may wish to write a media analysis about another cultural media portrayal. In either case, you are asked to perform a thoughtful, close analysis of the media source. In specific, in either case, you are asked to: 1) interpret the underlying messages or implications that exist within themedia source, and 2) interpret the effectiveness of the media source.

1 Hankerson Project Three: Culture and the African American Experience The Media Analysis This project will help you: ?develop your analytical skills. ?expand your understanding of media and how it operates. Background: For this project, we will examine select media representations of the African American culture. These media representations will further our understanding of how media portrayals–specifically African American media portrayals–operate. Ultimately, we will use this knowledge to engage with the overall task for this project which asks us to write a media analysis about a cultural media portrayal of interest. Task: As a frame for this project, we will draw from Afrobella’s DzAn Open Letter to Hip Hopdz which explores Afrobella’s perceptions of the state of hip hop. Your task for this project will be to compose a media analysis about Afrobella’s DzAn Open Letter to Hip Hop.dz Alternatively, you may wish to write a media analysis about another cultural media portrayal. In either case, you are asked to perform a thoughtful, close analysis of the media source. In specific, in either case, you are asked to: 1) interpret the underlying messages or implications that exist within themedia source, and 2) interpret the effectiveness of the media source.

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Fact Debate Brief Introduction Crime doesn’t pay; it should be punished. Even since childhood, a slap on the hand has prevented possible criminals from ever committing the same offense; whether it was successful or not depended on how much that child wanted that cookie. While a slap on the wrist might or might not be an effective deterrent, the same can be said about the death penalty. Every day, somewhere in the world, a criminal is stopped permanently from committing any future costs, but this is by the means of the death. While effective in stopping one person permanently, it does nothing about the crime world as a whole. While it is necessary to end the career of a criminal, no matter what his or her crime is, we must not end it by taking a life. Through this paper, the death penalty will be proven ineffective at deterring crime by use of other environmental factors. Definition: The death penalty is defined as the universal punishment of death as legally applied by a fair court system. It is important for it to be a fair legal system, as not to confuse it with genocide, mob mentality, or any other ruling without trial. Claim 1: Use of the death penalty is in decline Ground 1: According to the book The Death Penalty: A Worldwide Perspective by Roger Hood and Carolyn Hoyle, published Dec. 8th, 2014, the Oxford professors in criminology say “As in most of the rest of the world, the death penalty in the US is in decline and distributed unevenly in frequency of use” even addressing that, as of April 2014, 18 states no longer have a death penalty, and even Oregon and Washington are considering removing their death penalty laws. Furthermore, in 2013, only 9 of these states still retaining the death penalty actually executed someone. Warrant 1: The death penalty can be reinstated at any time, but so far, it hasn’t been. At the same time, more states consider getting rid of it altogether. Therefore, it becomes clear that even states don’t want to be involved with this process showing that this is a disliked process. Claim 2: Even states with death penalty in effect still have high crime rates. Ground 2: With the reports gathered from fbi.gov, lawstreetmedia.com, a website based around political expertise and research determined the ranking of each state based on violent crime, published September 12th, 2014. Of the top ten most violent states, only three of which had the death penalty instituted (Maryland #9, New Mexico #4, Alaska #3). The other seven still had the system in place, and, despite it, still have a high amount of violent crime. On the opposite end of the spectrum, at the bottom ten most violent states, four of which, including the bottom-most states, do not have the death penalty in place. Warrant 2: With this ranking, it literally proves that the death penalty does not deter crime, or that there is a correlation between having the death penalty and having a decrease in the crime rate. Therefore, the idea of death penalty deterring crime is a null term in the sense that there is no, or a flawed connection. Claim 3: Violent crime is decreasing (but not because if the death penalty) Ground 3 A: According to an article published by The Economist, dated July 23rd, 2013, the rate of violent crime is in fact decreasing, but not because of the death penalty, but rather, because we have more police. From 1995 to 2010, policing has increased one-fifth, and with it, a decline in crime rate. In fact, in cities such as Detroit where policing has been cut, an opposite effect, an increase in crime, has been reported. Ground 3 B: An article from the Wall Street Journal, dated May 28th, 2011, also cites a decline in violent, only this time, citing the reason as a correlation with poverty levels. In 2009, at the start of the housing crisis, crime rates also dropped noticeably. Oddly enough, this article points out the belief that unemployment is often associated with crime; instead, the evidence presented is environmental in nature. Warrant 3: Crime rate isn’t deterred by death penalty, but rather, our surroundings. Seeing as how conditions have improved, so has the state of peace. Therefore, it becomes clear that the death penalty is ineffective at deterring crime because other key factors present more possibility for improvement of society. Claim 4: The death penalty is a historically flawed system. Ground 4A: According to the book The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs by Scott Vollum, published in 2005, addresses how the case of the death penalty emerged to where it is today. While the book is now a decade old, it is used for historical context, particularly, in describing the first execution that took place in 1608. While it is true that most of these executions weren’t as well-grounded as the modern ones that take place now, they still had no effect in deterring crime. Why? Because even after America was established and more sane, the death penalty still had to be used because criminals still had violent behaviors. Ground 4B: According to data from Mother Jones, published May 17th, 2013, the reason why the crime rate was so high in the past could possibly be due to yet another environmental factor (affected by change over time), exposure to lead. Since the removal of lead from paint started over a hundred years ago, there has been a decline in homicide. Why is this important? Lead poisoning in child’s brain, if not lethal, can affect development and lead to mental disability, lower IQ, and lack of reasoning. Warrant 4: By examining history as a whole, there is a greater correlation between other factors that have resulted in a decline in violent crime. The decline in the crime rate has been an ongoing process, but has shown a faster decline due to other environmental factors, rather than the instatement of the death penalty. Claim 5: The world’s violent crime rate is changing, but not due to the death penalty. Ground 5A: According to article published by Amnesty USA in March of 2014, the number of executions under the death penalty reported in 2013 had increased by 15%. However, the rate of violent crime in the world has decreased significantly in the last decade. But, Latvia, for example, has permanently banned the death penalty since 2012. In 2014, the country was viewed overall as safe and low in violent crime rate. Ground 5B: However, while it is true that there is a decline in violent crime rate worldwide, The World Bank, April 17, 2013, reports that the rate of global poverty is decreasing. In a similar vein to the US, because wealth is being distributed better and conditions are improving overall, there is a steady decline in crime rate. Warrant 5: By examining the world as a whole, it becomes clear that it doesn’t matter if the death penalty is in place, violent crime will still exist. However, mirroring the US, as simple conditions improve, so does lifestyle. The death penalty does not deter crime in the world, rather a better quality of life is responsible for that. Works Cited “Death Sentences and Executions 2013.” Amnesty International USA. Amnesty USA, 26 Mar. 2014. Web. 15 Mar. 2015. <http://www.amnestyusa.org/research/reports/death-sentences-and-executions-2013>. D. K. “Why Is Crime Falling?” The Economist. The Economist Newspaper, 23 July 2013. Web. 12 Mar. 2015. <http://www.economist.com/blogs/economist-explains/2013/07/economist-explains-16>. Drum, Kevin. “The US Murder Rate Is on Track to Be Lowest in a Century.”Mother Jones. Mother Jones, 17 May 2013. Web. 13 Mar. 2015. <http://www.motherjones.com/kevin-drum/2013/05/us-murder-rate-track-be-lowest-century>. Hood, Roger, and Carolyn Hoyle. The Death Penalty: A Worldwide Perspective. Oxford: Oxford UP, 2002. 45. Print. Rizzo, Kevin. “Slideshow: America’s Safest and Most Dangerous States 2014.”Law Street Media. Law Street TM, 12 Sept. 2014. Web. 12 Mar. 2015. <http://lawstreetmedia.com/blogs/crime/safest-and-most-dangerous-states-2014/#slideshow>. Vollum, Scott. The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs. Newark, NJ: LexisNexis, 2005. 2. Print. Theis, David. “Remarkable Declines in Global Poverty, But Major Challenges Remain.” The World Bank. The World Bank, 17 Apr. 2013. Web. 15 Mar. 2015. <http://www.worldbank.org/en/news/press-release/2013/04/17/remarkable-declines-in-global-poverty-but-major-challenges-remain>. Wilson, James Q. “Hard Times, Fewer Crimes.” WSJ. The Wall Street Journal, 28 May 2011. Web. 13 Mar. 2015. <http://www.wsj.com/articles/SB10001424052702304066504576345553135009870>.

Fact Debate Brief Introduction Crime doesn’t pay; it should be punished. Even since childhood, a slap on the hand has prevented possible criminals from ever committing the same offense; whether it was successful or not depended on how much that child wanted that cookie. While a slap on the wrist might or might not be an effective deterrent, the same can be said about the death penalty. Every day, somewhere in the world, a criminal is stopped permanently from committing any future costs, but this is by the means of the death. While effective in stopping one person permanently, it does nothing about the crime world as a whole. While it is necessary to end the career of a criminal, no matter what his or her crime is, we must not end it by taking a life. Through this paper, the death penalty will be proven ineffective at deterring crime by use of other environmental factors. Definition: The death penalty is defined as the universal punishment of death as legally applied by a fair court system. It is important for it to be a fair legal system, as not to confuse it with genocide, mob mentality, or any other ruling without trial. Claim 1: Use of the death penalty is in decline Ground 1: According to the book The Death Penalty: A Worldwide Perspective by Roger Hood and Carolyn Hoyle, published Dec. 8th, 2014, the Oxford professors in criminology say “As in most of the rest of the world, the death penalty in the US is in decline and distributed unevenly in frequency of use” even addressing that, as of April 2014, 18 states no longer have a death penalty, and even Oregon and Washington are considering removing their death penalty laws. Furthermore, in 2013, only 9 of these states still retaining the death penalty actually executed someone. Warrant 1: The death penalty can be reinstated at any time, but so far, it hasn’t been. At the same time, more states consider getting rid of it altogether. Therefore, it becomes clear that even states don’t want to be involved with this process showing that this is a disliked process. Claim 2: Even states with death penalty in effect still have high crime rates. Ground 2: With the reports gathered from fbi.gov, lawstreetmedia.com, a website based around political expertise and research determined the ranking of each state based on violent crime, published September 12th, 2014. Of the top ten most violent states, only three of which had the death penalty instituted (Maryland #9, New Mexico #4, Alaska #3). The other seven still had the system in place, and, despite it, still have a high amount of violent crime. On the opposite end of the spectrum, at the bottom ten most violent states, four of which, including the bottom-most states, do not have the death penalty in place. Warrant 2: With this ranking, it literally proves that the death penalty does not deter crime, or that there is a correlation between having the death penalty and having a decrease in the crime rate. Therefore, the idea of death penalty deterring crime is a null term in the sense that there is no, or a flawed connection. Claim 3: Violent crime is decreasing (but not because if the death penalty) Ground 3 A: According to an article published by The Economist, dated July 23rd, 2013, the rate of violent crime is in fact decreasing, but not because of the death penalty, but rather, because we have more police. From 1995 to 2010, policing has increased one-fifth, and with it, a decline in crime rate. In fact, in cities such as Detroit where policing has been cut, an opposite effect, an increase in crime, has been reported. Ground 3 B: An article from the Wall Street Journal, dated May 28th, 2011, also cites a decline in violent, only this time, citing the reason as a correlation with poverty levels. In 2009, at the start of the housing crisis, crime rates also dropped noticeably. Oddly enough, this article points out the belief that unemployment is often associated with crime; instead, the evidence presented is environmental in nature. Warrant 3: Crime rate isn’t deterred by death penalty, but rather, our surroundings. Seeing as how conditions have improved, so has the state of peace. Therefore, it becomes clear that the death penalty is ineffective at deterring crime because other key factors present more possibility for improvement of society. Claim 4: The death penalty is a historically flawed system. Ground 4A: According to the book The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs by Scott Vollum, published in 2005, addresses how the case of the death penalty emerged to where it is today. While the book is now a decade old, it is used for historical context, particularly, in describing the first execution that took place in 1608. While it is true that most of these executions weren’t as well-grounded as the modern ones that take place now, they still had no effect in deterring crime. Why? Because even after America was established and more sane, the death penalty still had to be used because criminals still had violent behaviors. Ground 4B: According to data from Mother Jones, published May 17th, 2013, the reason why the crime rate was so high in the past could possibly be due to yet another environmental factor (affected by change over time), exposure to lead. Since the removal of lead from paint started over a hundred years ago, there has been a decline in homicide. Why is this important? Lead poisoning in child’s brain, if not lethal, can affect development and lead to mental disability, lower IQ, and lack of reasoning. Warrant 4: By examining history as a whole, there is a greater correlation between other factors that have resulted in a decline in violent crime. The decline in the crime rate has been an ongoing process, but has shown a faster decline due to other environmental factors, rather than the instatement of the death penalty. Claim 5: The world’s violent crime rate is changing, but not due to the death penalty. Ground 5A: According to article published by Amnesty USA in March of 2014, the number of executions under the death penalty reported in 2013 had increased by 15%. However, the rate of violent crime in the world has decreased significantly in the last decade. But, Latvia, for example, has permanently banned the death penalty since 2012. In 2014, the country was viewed overall as safe and low in violent crime rate. Ground 5B: However, while it is true that there is a decline in violent crime rate worldwide, The World Bank, April 17, 2013, reports that the rate of global poverty is decreasing. In a similar vein to the US, because wealth is being distributed better and conditions are improving overall, there is a steady decline in crime rate. Warrant 5: By examining the world as a whole, it becomes clear that it doesn’t matter if the death penalty is in place, violent crime will still exist. However, mirroring the US, as simple conditions improve, so does lifestyle. The death penalty does not deter crime in the world, rather a better quality of life is responsible for that. Works Cited “Death Sentences and Executions 2013.” Amnesty International USA. Amnesty USA, 26 Mar. 2014. Web. 15 Mar. 2015. . D. K. “Why Is Crime Falling?” The Economist. The Economist Newspaper, 23 July 2013. Web. 12 Mar. 2015. . Drum, Kevin. “The US Murder Rate Is on Track to Be Lowest in a Century.”Mother Jones. Mother Jones, 17 May 2013. Web. 13 Mar. 2015. . Hood, Roger, and Carolyn Hoyle. The Death Penalty: A Worldwide Perspective. Oxford: Oxford UP, 2002. 45. Print. Rizzo, Kevin. “Slideshow: America’s Safest and Most Dangerous States 2014.”Law Street Media. Law Street TM, 12 Sept. 2014. Web. 12 Mar. 2015. . Vollum, Scott. The Death Penalty: Constitutional Issues, Commentaries, and Case Briefs. Newark, NJ: LexisNexis, 2005. 2. Print. Theis, David. “Remarkable Declines in Global Poverty, But Major Challenges Remain.” The World Bank. The World Bank, 17 Apr. 2013. Web. 15 Mar. 2015. . Wilson, James Q. “Hard Times, Fewer Crimes.” WSJ. The Wall Street Journal, 28 May 2011. Web. 13 Mar. 2015. .

Fact Debate Brief Introduction Crime doesn’t pay; it should be … Read More...