Essay Assignment: Due December 6th, on Blackboard by 11:59 PM. Note: At least one draft (hardcopy, handed up in class) should be given to the instructor one week before due date (last date to give instructor draft is 1st December). If draft is not given, 20% will be taken off final grade for essay. Assignment Objective: This assignment is intended to provide you with the opportunity to reflect upon the course and material over the semester. Instructions: In this essay you will need think back prior to the semester and construct how you would have described ‘the self.’ Consider as your guide the many ways that the self has been studied over the course of the semester. For instance, you might consider the ways we have discussed: (1) the nature of the soul, (2) personal identity, (3) the relationship to others, (4) the ‘racial’ or ‘gendered’ self, (5) the self and freedom, (6) the social influences (economics, technology, and consumerism, for example) upon your self-development, etc. You should select one to two dimensions of the self and provide a description of what you thought about those prior to the course. Then, give a description of what you think about that or those dimension(s) of the self now. Be sure to reference the course material, either through the literature, or an author, or a driving concept from the course that you can explain in reference to the concept(s) you now hold. Within your discussion provide a comparison of what you thought prior to the course to what you now think of those dimension(s) of the self. In what ways has your conception of the ‘self’ changed, stayed the same, become enriched (or not). Be sure to give some explanation as to what has changed, or has not changed, and in what ways. Format: The paper should be in Times New Roman font, size 12, and double spaced. It should be about 1,200 words (approx. 4-5 pages). You will be required to have a bibliography and a cover page which includes the following: 1) The title of your paper. 2) Your name. 3) Your Student ID number. Citations: The recommended style of citation is Chicago (please see Blackboard for guidelines). You can use other styles if you like but the most important thing is to remain clear and consistent in the referencing style that you use. Please use at least 2-3 citations. Instruction for upload: Please upload it online onto Blackboard on the tab on the left hand side, entitled ‘Final Essay’ before midnight on December 6th. No hard copy is needed, but, as stated above, you will be required to give a hard copy of the draft at least one week before to the instructor. Grading: The final essay will be graded on: (1) how the instructions of the assignment were followed, (2) the accurateness and clarity in descriptions of course material (authors, core concepts, arguments, etc.), (3) the precision/correctness of writing, and (4) accuracy of referencing style.

Essay Assignment: Due December 6th, on Blackboard by 11:59 PM. Note: At least one draft (hardcopy, handed up in class) should be given to the instructor one week before due date (last date to give instructor draft is 1st December). If draft is not given, 20% will be taken off final grade for essay. Assignment Objective: This assignment is intended to provide you with the opportunity to reflect upon the course and material over the semester. Instructions: In this essay you will need think back prior to the semester and construct how you would have described ‘the self.’ Consider as your guide the many ways that the self has been studied over the course of the semester. For instance, you might consider the ways we have discussed: (1) the nature of the soul, (2) personal identity, (3) the relationship to others, (4) the ‘racial’ or ‘gendered’ self, (5) the self and freedom, (6) the social influences (economics, technology, and consumerism, for example) upon your self-development, etc. You should select one to two dimensions of the self and provide a description of what you thought about those prior to the course. Then, give a description of what you think about that or those dimension(s) of the self now. Be sure to reference the course material, either through the literature, or an author, or a driving concept from the course that you can explain in reference to the concept(s) you now hold. Within your discussion provide a comparison of what you thought prior to the course to what you now think of those dimension(s) of the self. In what ways has your conception of the ‘self’ changed, stayed the same, become enriched (or not). Be sure to give some explanation as to what has changed, or has not changed, and in what ways. Format: The paper should be in Times New Roman font, size 12, and double spaced. It should be about 1,200 words (approx. 4-5 pages). You will be required to have a bibliography and a cover page which includes the following: 1) The title of your paper. 2) Your name. 3) Your Student ID number. Citations: The recommended style of citation is Chicago (please see Blackboard for guidelines). You can use other styles if you like but the most important thing is to remain clear and consistent in the referencing style that you use. Please use at least 2-3 citations. Instruction for upload: Please upload it online onto Blackboard on the tab on the left hand side, entitled ‘Final Essay’ before midnight on December 6th. No hard copy is needed, but, as stated above, you will be required to give a hard copy of the draft at least one week before to the instructor. Grading: The final essay will be graded on: (1) how the instructions of the assignment were followed, (2) the accurateness and clarity in descriptions of course material (authors, core concepts, arguments, etc.), (3) the precision/correctness of writing, and (4) accuracy of referencing style.

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Member OBC and pulley C have a combined mass of 500 kg with mass center at G. Collar A provides horizontal support only. (a) Replace the 3kN force applied to the cable wrapped around the pulley by a force and a couple system at the center of the pulley (C). (5 points) (b) Draw a clear free body diagram of the member OBC after you have replaced the 3kN force by a force-couple system at C. (15 points) (c) Compute the reaction force at the collar A. (10 points) (d) Find the horizontal component of the reaction force supported by the pin at O. (10 points)

Member OBC and pulley C have a combined mass of 500 kg with mass center at G. Collar A provides horizontal support only. (a) Replace the 3kN force applied to the cable wrapped around the pulley by a force and a couple system at the center of the pulley (C). (5 points) (b) Draw a clear free body diagram of the member OBC after you have replaced the 3kN force by a force-couple system at C. (15 points) (c) Compute the reaction force at the collar A. (10 points) (d) Find the horizontal component of the reaction force supported by the pin at O. (10 points)

Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

Course: PHYS 5426 — Quantum Statistical Physics Assignment #1 Instructor: Gennady Y. Chitov Date Assigned: January 15, 2014 Due Date: January 29, 2014 Problem 1. Prove [a; f(a†)] = @f(a†) @a† (1) [a†; f(a)] = −@f(a) @a (2) for arbitrary function f of operator which admits a series expansion. The Bose creation/ annihilation operators satisfy the standard commutation relations [a; a†] ≡ aa† − a†a = 1 (3) Hint: From Eqs.(1,2) one can figure out the corresponding commutation relations for the powers of creation/annihilation operators and then prove them by the method of mathematical induction. Note that for an arbitrary operator Aˆ: @A^n @A^ = nAˆn−1. Problem 2. In the presence of a constant external force acting on a one-dimensional oscillating particle its Hamiltonian becomes that of the so-called displaced oscillator, and the Schr¨odinger equation ˆH (q) = E (q) of the problem (cf. lecture notes) can be written in terms of dimensionless variables as ( − 1 2 d2 d2 + 1 2 2 − √ 2  ) () = ” () ; (4) where q = √ ~ m! and E = ~!”. a). Write the Schr¨odinger equation (4) in terms of the creation/annihilation operators of the harmonic oscillator ( = 0)  = √1 2 (a + a†) (5) d d = √1 2 (a − a†) (6) 1 Via a linear transformation to the new creation/annihilation operators ˜a†; ˜a preserving the bosonic commutation relations for ˜a†; ˜a map the problem (4) of the displaced oscillator onto that of a simple harmonic oscillator with new operators (˜a†; ˜a). b). Find the spectrum (eigenvalues) ” (E) of the displaced oscillator. c). Write the normalized eigenstates |n⟩ of the displaced Hamiltonian (4) via a† and the vacuum state |Θ◦⟩ of the new operators, i.e. ˜a|Θ◦⟩ = 0 (7) d). As follows from the completeness of the oscillator’s eigenstates, the vacuum state of the displaced oscillator |Θ◦⟩ can be related to the simple oscillator’s vacuum |0⟩ (i.e., a|0⟩ = 0) as |Θ◦⟩ = Ω(a†)|0⟩ (8) Find (up to a normalization factor) the operator function Ω(a†) relating two vacua. Hint: in working out Eqs.(7,8), employ Eqs.(1,2). Problem 3. Prove from the standard commutation relations ([ai; a † j ]∓ = ij , etc) that ⟨0|aiaja † ka † l |0⟩ = jkil ± ikjl (9) the sign depending on the statistics. Also calculate the vacuum expectation value ⟨0|ahaiaja † ka † l a† m |0⟩. Problem 4. In the formalism of second quantization the two-particle interaction term of the Hamiltonian for spinless fermions is given by ˆ V = 1 2 ∫ ∫ dxdy ˆ †(x) ˆ †(y)V(x; y) ˆ (y) ˆ (x) (10) For the short-ranged interaction V(x; y) = V(|x−y|) ≡ V(r) = e2 exp(−r)=r find ˆ V in the momentum representation. The field operators and the creation/annihilation operators in the momentum representation are related in the usual way, i.e., ˆ †(x) = ∫ dp (2)3 a†(p)e−ipx (11) Note that the limit  → 0 recovers the Coulomb (long-ranged) interaction V(r) = e2=r. What is the Fourier transform V(q) of the Coulomb interaction? 2 Problem 5. The matrix elements of a two-particle interaction from the previous problem can be written as ⟨k3k4|V|k1k2⟩ = (2)3(k1 + k2 − k3 − k4)V(q) (12) where q ≡ k3−k1 is the momentum transfer. Show that the diagonal part of the interaction operator ˆ V found on the previous problem in the k-representation, arises from momentum transfers q = 0 and q = k2−k1. Write down the two interaction terms and identify them as direct (q = 0) and exchange (q = k2 − k1) interactions. Draw the corresponding Feynman diagrams. Problem 6. Find the first correction to the temperature dependence of the chemical potential  of the degenerate ideal electron gas, assuming constant particle concentration ⟨N⟩=V . Express the result in terms of T and the zero-temperature chemical potential ◦. For the calculations the following formula (we set kB = 1) can be used: I ≡ ∫ ∞ 0 f(“)d” e(“−)=T + 1 = ∫  0 f(“)d” + 2 6 T2f′() + O(T4) (13) 3

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CHM114: Exam #1 CHM 114, S2015 Exam #1, Version B Instructor: O. Graudejus Points: 100 Print Name Sign Name Student I.D. # 1. You are responsible for the information on this page. Please read it carefully. 2. If you enter your ASU ID incorrectly on the scantron, a 3 point penalty will be assessed. 3. Code your name and 10 digit affiliate identification number on the separate scantron answer sheet. Use only a #2 pencil 4. Do all calculations on the exam pages. Do not make any unnecessary marks on the answer sheet. 5. This exam consists of 25 multiple choice questions worth 4 points each and a periodic table. Make sure you have them all. 6. Choose the best answer to each of the questions and answer it on the computer-graded answer sheet. Read all responses before making a selection. 7. Read the directions carefully for each problem. 8. Avoid even casual glances at other students’ exams. 9. Stop writing and hand in your scantron answer sheet and your test promptly when instructed. LATE EXAMS MAY HAVE POINTS DEDUCTED. 10. You will have 50 minutes to complete the exam. 11. If you leave early, please do so quietly. 12. Work the easiest problems first. 13. A periodic table is attached as the last page to this exam. 14. Answers will be posted online this afternoon. Potentially useful information: K = ºC + 273.15 Avogadro’s Number = 6.022 × 1023 particles/mole 1amu = 1.66·10-24 g 1 cal=4.184 J \ -2- CHM 114: Exam #1 1) What volume (mL) of a concentrated solution of sodium hydroxide (6.00 M) must be diluted to 200.0 mL to make a 0.880 M solution of sodium hydroxide? A) 2.64 B) 176 C) 29.3 D) 26.4 E) 50.0 2) Sulfur and fluorine react in a combination reaction to produce sulfur hexafluoride: S (s) + 3 F2 (g)  SF6 (g) The maximum amount of SF6 that can be produced from the reaction of 3.5 g of sulfur with 4.5 g of fluorine is __________ g. A) 5.8 B) 3.2 C) 12 D) 16 E) 8.0 3) Of the reactions below, only __________ is not spontaneous. A) 2 2 Mg (s) 2HCl + (aq)®MgCl (aq) + H (g) B) 2 4 2 4 2 2Ni (s) + H SO (aq) ®Ni SO (aq) + H (g) C) 3 2 2Al (s) + 6HBr (aq)®2AlBr (aq) + 3H (g) D) 3 3 2 2Ag (s) + 2HNO (aq) ®2AgNO (aq) + H (g) E) 2 2 Zn (s) + 2HI (aq) ®ZnI (aq) + H (g) 4) Which solution has the same number of moles of NaOH as 40.00 mL of 0.100M solution of NaOH? A) 20.00 mL of 0.200M solution of NaOH B) 25.00 mL of 0.175M solution of NaOH C) 30.00 mL of 0.145M solution of NaOH D) 50.00 mL of 0.125M solution of NaOH E) 100.00 mL of 0.0500M solution of NaOH 5) What is the concentration (M) of a NaCl solution prepared by dissolving 9.3 g of NaCl in sufficient water to give 450 mL of solution? A) 0.35 B) 0.16 C) 0.45 D) 27 E) -2 2.7×10 -3- CHM 114: Exam #1 6) In which reaction does the oxidation number of hydrogen change? A) 2 HCl (aq) NaOH (+ aq)® NaCl (aq) + H O (l) B) 2 2 CaO (s) + H O (l) ®Ca(OH) (s) C) 4 3 4 2 2 2 2 HClO (aq) + CaCO (s) ® Ca(ClO ) (aq) + H O (l) +CO (g) D) 2 2 2 3 SO (g) + H O (l)®H SO (aq) E) 2 2 2 Na (s) + 2H O (l) ® 2 NaOH (aq) + H (g) 7) Which atom has the smallest number of neutrons? A) phosphorus-30 B) chlorine-37 C) potassium-39 D) argon-40 E) calcium-40 8) The change in the internal energy of a system that absorbs 2,500 J of heat and that has received 7,655 J of work by the surroundings is __________ J. A) -10,155 B) -5,155 C) 7 −1.91×10 D) 10,155 E) 5,155 9) When a metal and a nonmetal react, the __________ tends to lose electrons and the __________ tends to gain electrons. A) metal, metal B) nonmetal, nonmetal C) metal, nonmetal D) nonmetal, metal E) None of the above, these elements share electrons. 10) What is the oxidation number of nitrogen in HNO2? A) -5 B) -3 C) 0 D) +3 E) +5 -4- CHM 114: Exam #1 11) Elements in Group 7A are known as the __________. A) chalcogens B) alkaline earth metals C) alkali metals D) halogens E) noble gases 12) The concentration of iodide ions in a 0.193 M solution of sodium iodide is __________. A) 0.193 M B) 0.386 M C) 0.0965 M D) 0.579 M E) 0.0643 M 13) Lithium and nitrogen react to produce lithium nitride: 6Li (s) + N2 (g)  2Li3N (s) How many moles of N2 are needed to react with 1.422 mol of lithium? A) 4.26 B) 0.710 C) 0.237 D) 2.13 E) 0.118 14) The balanced equation for the decomposition of sodium azide is __________. A) 2NaN3 (s)  Na2 (s) + 3 N2 (g) B) NaN3 (s)  Na (s) + N2 (g) C) 2NaN3 (s)  2Na (s) + 3 N2 (g) D) NaN3 (s)  Na (s) + N2 (g) + N (g) E) 2NaN3 (s)  2Na (s) + 2 N2 (g) 15) A sample of CH2F2 with a mass of 9.5 g contains __________ atoms of F. A) 2.2 × 1023 B) 38 C) 3.3 × 1024 D) 4.4 × 1023 E) 9.5 -5- CHM 114: Exam #1 16) An unknown element is found to have three naturally occurring isotopes with atomic masses of 35.9675 (0.337%), 37.9627 (0.063%), and 39.9624 (99.600%). Which of the following is the unknown element? A) Ar B) K C) Cl D) Ca E) None of the above could be the unknown element. 17) The value of DH° for the reaction below is -482 kJ. Calculate the heat (kJ) released to the surroundings when 24.0 g of CO (g) reacts completely. 2 2 2CO(g) +O (g)®2CO (g) A) 3 2.89×10 B) 207 C) 103 D) 65.7 E) -482 18) Lead (II) carbonate decomposes to give lead (II) oxide and carbon dioxide: PbCO3 (s)  PbO (s) + CO2 (g) __________ grams of carbondioxide will be produced by the decomposition of 7.50 g of lead (II) carbonate? A) 1.23 B) 2.50 C) 0.00936 D) 6.26 E) 7.83 19) Combining aqueous solutions of BaCl2 and K2SO4 affords a precipitate of 4 BaSO . Which ion(s) is/are spectator ions in the reaction? A) 2 Ba only + B) K+ only C) 2 2 Ba and SO4 + − D) SO4 2- and Cl- E) K+ and Cl- 20) Which combination will produce a precipitate? A) Pb(NO3)2 (aq) and HCl (aq) B) Cu(NO3)2 (aq) and KCl (aq) C) KOH (aq) and HNO3 (aq) D) AgNO3 (aq) and HNO3 (aq) E) NaOH (aq) and Sr(NO3)2 (aq) -6- CHM 114: Exam #1 21) There are __________ sulfur atoms in 50 molecules of C4H4S2. A) 1.5 × 1025 B) 100 C) 3.0 × 1025 D) 50 E) 6.02 × 1023 22) A compound contains 38.7% K, 13.9% N, and 47.4% O by mass. What is the empirical formula of the compound? A) K2N2O3 B) KNO2 C) KNO3 D) K2NO3 E) K4NO5 23) Predict the empirical formula of the ionic compound that forms from sodium and fluorine. A) 2 Na F B) 2 NaF C) 2 3 Na F D) NaF E) 3 2 Na F 24) The mass % of Krypton in the binary compound KrF2 is __________. A) 18.48 B) 45.38 C) 68.80 D) 81.52 E) 31.20 25) The correct name for K2SO3 is __________. A) potassium sulfate B) potassium disulfide C) potassium sulfite D) potassium sulfide E) dipotassium sulfate -7- CHM 114: Exam #1

CHM114: Exam #1 CHM 114, S2015 Exam #1, Version B Instructor: O. Graudejus Points: 100 Print Name Sign Name Student I.D. # 1. You are responsible for the information on this page. Please read it carefully. 2. If you enter your ASU ID incorrectly on the scantron, a 3 point penalty will be assessed. 3. Code your name and 10 digit affiliate identification number on the separate scantron answer sheet. Use only a #2 pencil 4. Do all calculations on the exam pages. Do not make any unnecessary marks on the answer sheet. 5. This exam consists of 25 multiple choice questions worth 4 points each and a periodic table. Make sure you have them all. 6. Choose the best answer to each of the questions and answer it on the computer-graded answer sheet. Read all responses before making a selection. 7. Read the directions carefully for each problem. 8. Avoid even casual glances at other students’ exams. 9. Stop writing and hand in your scantron answer sheet and your test promptly when instructed. LATE EXAMS MAY HAVE POINTS DEDUCTED. 10. You will have 50 minutes to complete the exam. 11. If you leave early, please do so quietly. 12. Work the easiest problems first. 13. A periodic table is attached as the last page to this exam. 14. Answers will be posted online this afternoon. Potentially useful information: K = ºC + 273.15 Avogadro’s Number = 6.022 × 1023 particles/mole 1amu = 1.66·10-24 g 1 cal=4.184 J \ -2- CHM 114: Exam #1 1) What volume (mL) of a concentrated solution of sodium hydroxide (6.00 M) must be diluted to 200.0 mL to make a 0.880 M solution of sodium hydroxide? A) 2.64 B) 176 C) 29.3 D) 26.4 E) 50.0 2) Sulfur and fluorine react in a combination reaction to produce sulfur hexafluoride: S (s) + 3 F2 (g)  SF6 (g) The maximum amount of SF6 that can be produced from the reaction of 3.5 g of sulfur with 4.5 g of fluorine is __________ g. A) 5.8 B) 3.2 C) 12 D) 16 E) 8.0 3) Of the reactions below, only __________ is not spontaneous. A) 2 2 Mg (s) 2HCl + (aq)®MgCl (aq) + H (g) B) 2 4 2 4 2 2Ni (s) + H SO (aq) ®Ni SO (aq) + H (g) C) 3 2 2Al (s) + 6HBr (aq)®2AlBr (aq) + 3H (g) D) 3 3 2 2Ag (s) + 2HNO (aq) ®2AgNO (aq) + H (g) E) 2 2 Zn (s) + 2HI (aq) ®ZnI (aq) + H (g) 4) Which solution has the same number of moles of NaOH as 40.00 mL of 0.100M solution of NaOH? A) 20.00 mL of 0.200M solution of NaOH B) 25.00 mL of 0.175M solution of NaOH C) 30.00 mL of 0.145M solution of NaOH D) 50.00 mL of 0.125M solution of NaOH E) 100.00 mL of 0.0500M solution of NaOH 5) What is the concentration (M) of a NaCl solution prepared by dissolving 9.3 g of NaCl in sufficient water to give 450 mL of solution? A) 0.35 B) 0.16 C) 0.45 D) 27 E) -2 2.7×10 -3- CHM 114: Exam #1 6) In which reaction does the oxidation number of hydrogen change? A) 2 HCl (aq) NaOH (+ aq)® NaCl (aq) + H O (l) B) 2 2 CaO (s) + H O (l) ®Ca(OH) (s) C) 4 3 4 2 2 2 2 HClO (aq) + CaCO (s) ® Ca(ClO ) (aq) + H O (l) +CO (g) D) 2 2 2 3 SO (g) + H O (l)®H SO (aq) E) 2 2 2 Na (s) + 2H O (l) ® 2 NaOH (aq) + H (g) 7) Which atom has the smallest number of neutrons? A) phosphorus-30 B) chlorine-37 C) potassium-39 D) argon-40 E) calcium-40 8) The change in the internal energy of a system that absorbs 2,500 J of heat and that has received 7,655 J of work by the surroundings is __________ J. A) -10,155 B) -5,155 C) 7 −1.91×10 D) 10,155 E) 5,155 9) When a metal and a nonmetal react, the __________ tends to lose electrons and the __________ tends to gain electrons. A) metal, metal B) nonmetal, nonmetal C) metal, nonmetal D) nonmetal, metal E) None of the above, these elements share electrons. 10) What is the oxidation number of nitrogen in HNO2? A) -5 B) -3 C) 0 D) +3 E) +5 -4- CHM 114: Exam #1 11) Elements in Group 7A are known as the __________. A) chalcogens B) alkaline earth metals C) alkali metals D) halogens E) noble gases 12) The concentration of iodide ions in a 0.193 M solution of sodium iodide is __________. A) 0.193 M B) 0.386 M C) 0.0965 M D) 0.579 M E) 0.0643 M 13) Lithium and nitrogen react to produce lithium nitride: 6Li (s) + N2 (g)  2Li3N (s) How many moles of N2 are needed to react with 1.422 mol of lithium? A) 4.26 B) 0.710 C) 0.237 D) 2.13 E) 0.118 14) The balanced equation for the decomposition of sodium azide is __________. A) 2NaN3 (s)  Na2 (s) + 3 N2 (g) B) NaN3 (s)  Na (s) + N2 (g) C) 2NaN3 (s)  2Na (s) + 3 N2 (g) D) NaN3 (s)  Na (s) + N2 (g) + N (g) E) 2NaN3 (s)  2Na (s) + 2 N2 (g) 15) A sample of CH2F2 with a mass of 9.5 g contains __________ atoms of F. A) 2.2 × 1023 B) 38 C) 3.3 × 1024 D) 4.4 × 1023 E) 9.5 -5- CHM 114: Exam #1 16) An unknown element is found to have three naturally occurring isotopes with atomic masses of 35.9675 (0.337%), 37.9627 (0.063%), and 39.9624 (99.600%). Which of the following is the unknown element? A) Ar B) K C) Cl D) Ca E) None of the above could be the unknown element. 17) The value of DH° for the reaction below is -482 kJ. Calculate the heat (kJ) released to the surroundings when 24.0 g of CO (g) reacts completely. 2 2 2CO(g) +O (g)®2CO (g) A) 3 2.89×10 B) 207 C) 103 D) 65.7 E) -482 18) Lead (II) carbonate decomposes to give lead (II) oxide and carbon dioxide: PbCO3 (s)  PbO (s) + CO2 (g) __________ grams of carbondioxide will be produced by the decomposition of 7.50 g of lead (II) carbonate? A) 1.23 B) 2.50 C) 0.00936 D) 6.26 E) 7.83 19) Combining aqueous solutions of BaCl2 and K2SO4 affords a precipitate of 4 BaSO . Which ion(s) is/are spectator ions in the reaction? A) 2 Ba only + B) K+ only C) 2 2 Ba and SO4 + − D) SO4 2- and Cl- E) K+ and Cl- 20) Which combination will produce a precipitate? A) Pb(NO3)2 (aq) and HCl (aq) B) Cu(NO3)2 (aq) and KCl (aq) C) KOH (aq) and HNO3 (aq) D) AgNO3 (aq) and HNO3 (aq) E) NaOH (aq) and Sr(NO3)2 (aq) -6- CHM 114: Exam #1 21) There are __________ sulfur atoms in 50 molecules of C4H4S2. A) 1.5 × 1025 B) 100 C) 3.0 × 1025 D) 50 E) 6.02 × 1023 22) A compound contains 38.7% K, 13.9% N, and 47.4% O by mass. What is the empirical formula of the compound? A) K2N2O3 B) KNO2 C) KNO3 D) K2NO3 E) K4NO5 23) Predict the empirical formula of the ionic compound that forms from sodium and fluorine. A) 2 Na F B) 2 NaF C) 2 3 Na F D) NaF E) 3 2 Na F 24) The mass % of Krypton in the binary compound KrF2 is __________. A) 18.48 B) 45.38 C) 68.80 D) 81.52 E) 31.20 25) The correct name for K2SO3 is __________. A) potassium sulfate B) potassium disulfide C) potassium sulfite D) potassium sulfide E) dipotassium sulfate -7- CHM 114: Exam #1

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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write the absolute value of each nuber and explian your reasoning. numbers: integer- +5 negative fraction- -1/2 posative fraction- 1/3 negative decimal- -.2 positive decimal- +08

write the absolute value of each nuber and explian your reasoning. numbers: integer- +5 negative fraction- -1/2 posative fraction- 1/3 negative decimal- -.2 positive decimal- +08

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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...
Laurentian University ENGR 1056: Applied Mechanics I 2015{2016 Assignment #2 Instructions: Complete all the questions. Show your work as marks are given for process. Submit your assignment as a single PDF le to the appropriate dropbox on D2L. You may use the photocopiers in the library as scanners if you do not have access to a scanner. Ensure that the scans are readable. Late assignments will NOT be accepted. Due: Tues. Sept. 29, 2015, 8:30am 2-1. Assuming that: A = 5i ? 3j + 2k B = ?2i + 2k then calculate the following and report your answers to 3 signi cant gures: (a) eA; (b) A  B; (c) B  A; and, (d) the component of A parallel to B. 2-2. Do question 2.159 from your text. Report your answers to four signi cant digits. 2-3. You are given the following directions: start at point A, walk north 5 ft to point B, turn 30 degrees to your right, walk forward for 8 ft to point C, turn 15 degrees to your right, walk forward x ft to point D. If the distance directly from A to D is 16 ft, what is the value of x? What is the angle  between AB and AD? Include a diagram of your route. Label your diagram with points A to D and the angle . Report you answers to 3 signi cant digits. 2-4. Do question 2.165 from your text. Report your answers in newtons to four signi - cant gures. W. Brent Lievers 2015-09-21 Page 1 of 1

Laurentian University ENGR 1056: Applied Mechanics I 2015{2016 Assignment #2 Instructions: Complete all the questions. Show your work as marks are given for process. Submit your assignment as a single PDF le to the appropriate dropbox on D2L. You may use the photocopiers in the library as scanners if you do not have access to a scanner. Ensure that the scans are readable. Late assignments will NOT be accepted. Due: Tues. Sept. 29, 2015, 8:30am 2-1. Assuming that: A = 5i ? 3j + 2k B = ?2i + 2k then calculate the following and report your answers to 3 signi cant gures: (a) eA; (b) A  B; (c) B  A; and, (d) the component of A parallel to B. 2-2. Do question 2.159 from your text. Report your answers to four signi cant digits. 2-3. You are given the following directions: start at point A, walk north 5 ft to point B, turn 30 degrees to your right, walk forward for 8 ft to point C, turn 15 degrees to your right, walk forward x ft to point D. If the distance directly from A to D is 16 ft, what is the value of x? What is the angle  between AB and AD? Include a diagram of your route. Label your diagram with points A to D and the angle . Report you answers to 3 signi cant digits. 2-4. Do question 2.165 from your text. Report your answers in newtons to four signi - cant gures. W. Brent Lievers 2015-09-21 Page 1 of 1