The following equation can be used to compute values of y as a function of x: y = b  e?ax  sin(b  x)  (0:012  x4 ? 0:15  x3 + 0:075  x2 + 2:5  x) where a and b are parameters. Write the equation for implementation with MATLAB, where a = 2, b = 5, and x is a vector holding values from 0 to =24 in increments of x = =40. Employ the minimum number of periods (i.e., dot notation) so that your formulation yields a vector for y. In addition, compute the vector z = y2 where each element holds the square of each element of y. Combine x, y, and z into a matrix w, where each column holds one of the variables, and display w using the short g format. In addition, generate a labeled plot of y and z versus x. Include a legend on the plot (use help to understand how to do this). For y, use a 1:5-point, dashdotted red line with 14-point, red-edged white-faced pentagram-shaped markers. For z, use a standard-sized (i.e., default) solid blue line with standard-sized, blue-edged, green-faced square markers.

## The following equation can be used to compute values of y as a function of x: y = b  e?ax  sin(b  x)  (0:012  x4 ? 0:15  x3 + 0:075  x2 + 2:5  x) where a and b are parameters. Write the equation for implementation with MATLAB, where a = 2, b = 5, and x is a vector holding values from 0 to =24 in increments of x = =40. Employ the minimum number of periods (i.e., dot notation) so that your formulation yields a vector for y. In addition, compute the vector z = y2 where each element holds the square of each element of y. Combine x, y, and z into a matrix w, where each column holds one of the variables, and display w using the short g format. In addition, generate a labeled plot of y and z versus x. Include a legend on the plot (use help to understand how to do this). For y, use a 1:5-point, dashdotted red line with 14-point, red-edged white-faced pentagram-shaped markers. For z, use a standard-sized (i.e., default) solid blue line with standard-sized, blue-edged, green-faced square markers.

Homework 1 Q.1 what is product of these matrices? [■(3&2&6@-2&1&0@4&1&0)] ■(2@3@4) 6 Q.2 what is largest number of pivots a 7×5 matrix can have? Q.3 find standard matrix of linear transformation T: R^2→R^2 which rotates a point about the origion through an angle of π/4 radians. Q.4 True or False If matrices A and B are equivalent, they have same reduced echelon form In general A+B≠B+A I matrix A is symmetric then so is A+I_n A matrix A must be a square matrix to be invertible. If det (A) ≠ 0 then column of A are linearly independent. If n × n matrix is equivalent to I_n then A^(-1) is also equivalent toI_n. If m × n matrix has pivot position in every row then the equation Ax = b has a unique solution for each b in R^m If AB = I, then I is invertible.

## Homework 1 Q.1 what is product of these matrices? [■(3&2&6@-2&1&0@4&1&0)] ■(2@3@4) 6 Q.2 what is largest number of pivots a 7×5 matrix can have? Q.3 find standard matrix of linear transformation T: R^2→R^2 which rotates a point about the origion through an angle of π/4 radians. Q.4 True or False If matrices A and B are equivalent, they have same reduced echelon form In general A+B≠B+A I matrix A is symmetric then so is A+I_n A matrix A must be a square matrix to be invertible. If det (A) ≠ 0 then column of A are linearly independent. If n × n matrix is equivalent to I_n then A^(-1) is also equivalent toI_n. If m × n matrix has pivot position in every row then the equation Ax = b has a unique solution for each b in R^m If AB = I, then I is invertible.

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For Day 19 Homework Cover Sheet Name:_________________________________________________ Read Pages from 294-315, or watch the videos listed below Introduction to Division http://www.youtube.com/watch?v=7gZ4yW1nr9Y (13 min) Introduction to Division of Rational Numbers http://www.youtube.com/watch?v=9LTICGxqwKE (10 min) Division of Decimal Numbers and Rational Expressions http://www.youtube.com/watch?v=BGReDOGObbk (7 min) Division Algorithm for Decimal Numbers and Polynomials http://www.youtube.com/watch?v=XXr0ixy8PfA (8 min) Division Algorithm for Decimal Polynomials http://www.youtube.com/watch?v=PQrlt8PhFAE (11 min) Attempt problems from workbook pages 91-97 Summary of the lectures you watched should include answers to the following questions. When doing division of rational expressions or numbers, what allows us to multiply by the reciprocal of the divisor instead? For example, 3/4÷3/5=3/4×5/3 or (x^2-1)/x÷(x+1)/(x-2)=(x^2-1)/x×(x-2)/(x-1) List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- List the number for the ALEKS topics you were stuck on from the list at the end of the video logs-   ALEKS Topics Mastered Division facts Division involving a whole number and a fraction Division involving quotients with intermediate zeros Division of a decimal by a power of ten Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division without carry Fraction division Integer multiplication and division Multiplying or dividing numbers written in scientific notation Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Rationalizing the denominator of a radical expression Simplifying a product and quotient involving square roots of negative numbers The reciprocal of a number Writing a ratio as a percentage without a calculator

## For Day 19 Homework Cover Sheet Name:_________________________________________________ Read Pages from 294-315, or watch the videos listed below Introduction to Division http://www.youtube.com/watch?v=7gZ4yW1nr9Y (13 min) Introduction to Division of Rational Numbers http://www.youtube.com/watch?v=9LTICGxqwKE (10 min) Division of Decimal Numbers and Rational Expressions http://www.youtube.com/watch?v=BGReDOGObbk (7 min) Division Algorithm for Decimal Numbers and Polynomials http://www.youtube.com/watch?v=XXr0ixy8PfA (8 min) Division Algorithm for Decimal Polynomials http://www.youtube.com/watch?v=PQrlt8PhFAE (11 min) Attempt problems from workbook pages 91-97 Summary of the lectures you watched should include answers to the following questions. When doing division of rational expressions or numbers, what allows us to multiply by the reciprocal of the divisor instead? For example, 3/4÷3/5=3/4×5/3 or (x^2-1)/x÷(x+1)/(x-2)=(x^2-1)/x×(x-2)/(x-1) List any parts of the video lecture (if there are any) that were unclear or you had trouble understanding. Please be specific and do not just say “All of it”. Questions you had difficulty with or felt stuck on- List the number for the ALEKS topics you were stuck on from the list at the end of the video logs-   ALEKS Topics Mastered Division facts Division involving a whole number and a fraction Division involving quotients with intermediate zeros Division of a decimal by a power of ten Division with carry Division with trailing zeros: Problem type 1 Division with trailing zeros: Problem type 2 Division without carry Fraction division Integer multiplication and division Multiplying or dividing numbers written in scientific notation Quotient and remainder: Problem type 1 Quotient and remainder: Problem type 2 Quotient and remainder: Problem type 3 Rationalizing the denominator of a radical expression Simplifying a product and quotient involving square roots of negative numbers The reciprocal of a number Writing a ratio as a percentage without a calculator

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Comp755 HW 2 – Fall 2015 1. Problem 4.2 (10pts) 2. Problem 4.4 (15pts) 3. Problem 5.25 (10pts) 4. Problem 10.2 (15pts) . Hint: Create three Gantt charts where each square represents 10 time units. a. The first chart should use earliest deadline using the processes that are currently available. Since there is no preemption, some processes will not be scheduled if there start deadline is missed. b. The second chart should schedule strictly by the earliest deadline. The processor will be idle if the process with the earliest deadline has not arrived. c. The third chart should just use FCFS. 5. (Synchronize threads) Write a program that launches 1,000 threads. Each thread adds 1 to a variable sum that initially is 0. You need to pass sum by reference to each thread. In order to pass it by reference, define an Integer wrapper object to hold sum. Run the program with and without synchronization to see its effect (Create a command line argument where passing a 0 means run unsynchronized and passing a 1 means to run synchronized). Submit your entire Netbeans project (50pts).

## Comp755 HW 2 – Fall 2015 1. Problem 4.2 (10pts) 2. Problem 4.4 (15pts) 3. Problem 5.25 (10pts) 4. Problem 10.2 (15pts) . Hint: Create three Gantt charts where each square represents 10 time units. a. The first chart should use earliest deadline using the processes that are currently available. Since there is no preemption, some processes will not be scheduled if there start deadline is missed. b. The second chart should schedule strictly by the earliest deadline. The processor will be idle if the process with the earliest deadline has not arrived. c. The third chart should just use FCFS. 5. (Synchronize threads) Write a program that launches 1,000 threads. Each thread adds 1 to a variable sum that initially is 0. You need to pass sum by reference to each thread. In order to pass it by reference, define an Integer wrapper object to hold sum. Run the program with and without synchronization to see its effect (Create a command line argument where passing a 0 means run unsynchronized and passing a 1 means to run synchronized). Submit your entire Netbeans project (50pts).

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A square loop of wire with a small resistance is moved with constant speed from a field free region into a region of uniform B field (B is constant in time) and then back into a field free region to the left. The self inductance of loop is negligible. QUESTION: A) When leaving the field the coil experiences a magnetic force to the left. B) While the loop is entirely in the field, the emf in the loop is zero. C) When entering the field the coil experiences a magnetic force to the right. D) Upon leaving the field, a clockwise current flows in the loop. E) Upon entering the field, a clockwise current flows in the loop.

## A square loop of wire with a small resistance is moved with constant speed from a field free region into a region of uniform B field (B is constant in time) and then back into a field free region to the left. The self inductance of loop is negligible. QUESTION: A) When leaving the field the coil experiences a magnetic force to the left. B) While the loop is entirely in the field, the emf in the loop is zero. C) When entering the field the coil experiences a magnetic force to the right. D) Upon leaving the field, a clockwise current flows in the loop. E) Upon entering the field, a clockwise current flows in the loop.

A six- turn square loop of sides 0.2 m lies in a plane perpendicular to a uniform magnetic field of magnitude 0.5 T. If the wire reshaped into a three- turn square of sides 0.4 m in 0.1 sec, what is the magnitude of the emf induced in wire during this time ? 1) 0.68 volts 2) 1.2 volts 3) 2.4 volts 4) 3.6 volts 5) 4.8 volts.

## A six- turn square loop of sides 0.2 m lies in a plane perpendicular to a uniform magnetic field of magnitude 0.5 T. If the wire reshaped into a three- turn square of sides 0.4 m in 0.1 sec, what is the magnitude of the emf induced in wire during this time ? 1) 0.68 volts 2) 1.2 volts 3) 2.4 volts 4) 3.6 volts 5) 4.8 volts.

Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1  4 −2 1 3  is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0   2346  (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : →  which rotates a point about the origin through an angle of   radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices  and  are row equivalent, they have the same reduced echelon form. In general,  +  ≠  +  (assume  and  are  x  matrices). If a matrix  is symmetric, then so is  + “#. A matrix  must be a square matrix to be invertible. If \$%&’( ≠ 0, then columns of  are linearly independent. If an  x  matrix  is equivalent to “#, then )* is also equivalent to “#. If an + x  matrix  has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If  = “, then  is invertible.

## Math 285 Quiz One Name: ________________ 1. The product of these two matrices 5 2 2 −1  4 −2 1 3  is (Please show your work for full credit.) 2. For what value of a is this determinant equal to 0? 0 5 2 0 1 −8 −4 2 (please justify your answer.) 3. What is the product of these matrices? 3 2 6 −2 1 0 4 1 0   2346  (Please justify your answer.) 4. What is the largest possible number of pivots a 7 × 5 matrix can have? (Please justify your answer.) Homework 1 5. Find the standard matrix of the linear transformation : →  which rotates a point about the origin through an angle of   radians (counterclockwise). True or False (Simply enter T or F, no need to justify the answer) If matrices  and  are row equivalent, they have the same reduced echelon form. In general,  +  ≠  +  (assume  and  are  x  matrices). If a matrix  is symmetric, then so is  + “#. A matrix  must be a square matrix to be invertible. If \$%&’( ≠ 0, then columns of  are linearly independent. If an  x  matrix  is equivalent to “#, then )* is also equivalent to “#. If an + x  matrix  has a pivot position in every row, then the equation , = . has a unique solution for each . in /0. If  = “, then  is invertible.

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