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Exam 12: Vectors and Matrices

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Exam 1: Linear Functions and Change125 Questionsadd course
Exam 2: Functions107 Questionsadd course
Exam 3: Quadratic Functions41 Questionsadd course
Exam 4: Exponential Functions102 Questionsadd course
Exam 5: Logarithmic Functions79 Questionsadd course
Exam 6: Transformations of Functions and Their Graphs100 Questionsadd course
Exam 7: Trigonometry in Circles and Triangles120 Questionsadd course
Exam 8: Trigonometric Functions120 Questionsadd course
Exam 9: Trigonometric Identities and Their Applications60 Questionsadd course
Exam 10: Compositions, Inverses, and Combinations of Functions64 Questionsadd course
Exam 11: Polynomial and Rational Functions143 Questionsadd course
Exam 12: Vectors and Matrices102 Questionsadd course
Exam 13: Sequences and Series81 Questionsadd course
Exam 14: Parametric Equations and Conic Sections120 Questionsadd course
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A car travels 19 miles south and then 24 miles east. Which of the following is true?

(Multiple Choice)
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Question 21

The vectors The vectors and are parallel. and The vectors and are parallel. are parallel.

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Question 22

Three people stand in the middle of a field. The first person walks 11 yards north and then 14 yards east. The second person remains where he is. The third person walks 18 yards north and then 8 yards east. The angle formed by drawing a line from the first person to the second person to the third person is _____ Three people stand in the middle of a field. The first person walks 11 yards north and then 14 yards east. The second person remains where he is. The third person walks 18 yards north and then 8 yards east. The angle formed by drawing a line from the first person to the second person to the third person is _____ . Round to the nearest whole number. . Round to the nearest whole number.

(Short Answer)
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Question 23

Let Let and .Find . and Let and .Find . .Find Let and .Find . .

(Short Answer)
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Question 24

A) A+B B) C) D) E) F) A) A+B B) A) A+B B) C) D) E) F) C) A) A+B B) C) D) E) F) D) A) A+B B) C) D) E) F) E) A) A+B B) C) D) E) F) F) A) A+B B) C) D) E) F)

(Short Answer)
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Question 25

Let Let and . A) Find B) C) and Let and . A) Find B) C) . A) Find Let and . A) Find B) C) B) Let and . A) Find B) C) C) Let and . A) Find B) C)

(Short Answer)
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Question 26

An airplane is flying at an airspeed of 660 km/hr in a crosswind blowing from the southeast at a speed of 60 km/hr. To end up going due east, the plane should head _____ An airplane is flying at an airspeed of 660 km/hr in a crosswind blowing from the southeast at a speed of 60 km/hr. To end up going due east, the plane should head _____ south of east and will have a speed of ______km/hr relative to the ground. Round each answer to 2 decimal places. south of east and will have a speed of ______km/hr relative to the ground. Round each answer to 2 decimal places.

(Short Answer)
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Question 27

A retailer's total monthly sales of three different models of television is given by the vector A retailer's total monthly sales of three different models of television is given by the vector . If the sales for each model go up by 8 the next month, what is , the next month's total sales? . If the sales for each model go up by 8 the next month, what is A retailer's total monthly sales of three different models of television is given by the vector . If the sales for each model go up by 8 the next month, what is , the next month's total sales? , the next month's total sales?

(Short Answer)
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Question 28

Jack and Jill begin walking away from a water well. Jill walks 6 meters north, and then 12 meters northeast. When Jill stops, Jack is half as far from the well as she is. How far is Jack from the well?

(Short Answer)
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Question 29

Given that Given that and , let , where . What is ? and Given that and , let , where . What is ? , let Given that and , let , where . What is ? , where Given that and , let , where . What is ? . What is Given that and , let , where . What is ? ?

(Short Answer)
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Question 30

For what value of x are For what value of x are and parallel? and For what value of x are and parallel? parallel?

(Short Answer)
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Question 31

Let Let and .Find . and Let and .Find . .Find Let and .Find . .

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Question 32

In certain cases, there is a nonzero vector In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? and a scalar In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? for a matrix In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? such that In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? . The vector In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? is called an eigenvector of In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? with eigenvalue In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? . Let In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? with eigenvector In certain cases, there is a nonzero vector and a scalar for a matrix such that . The vector is called an eigenvector of with eigenvalue . Let with eigenvector . What is its eigenvalue? . What is its eigenvalue?

(Short Answer)
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Question 33

The vector starting at the point P = (0, 2) and ending at the point Q = (1, 4) can be resolved into the components The vector starting at the point P = (0, 2) and ending at the point Q = (1, 4) can be resolved into the components

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Question 34

Find the length of the vector Find the length of the vector to 3 decimal places. to 3 decimal places.

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Question 35

Let Let be a vector of length 3 pointing north of east. Find the length and direction of . be a vector of length 3 pointing Let be a vector of length 3 pointing north of east. Find the length and direction of . north of east. Find the length and direction of Let be a vector of length 3 pointing north of east. Find the length and direction of . .

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Question 36

A country has two main political parties. The vector A country has two main political parties. The vector Gives the number of people who are members of the first party, the second party, and neither party, respectively. Suppose . Which party's members are the most loyal?Gives the number of people who are members of the first party, the second party, and neither party, respectively. Suppose A country has two main political parties. The vector Gives the number of people who are members of the first party, the second party, and neither party, respectively. Suppose . Which party's members are the most loyal? . Which party's members are the most loyal?

(Multiple Choice)
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Question 37

Let the vector Let the vector describe a triangle with vertices at , , and . If the triangle is rotated through an angle of 28 clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places. describe a triangle with vertices at Let the vector describe a triangle with vertices at , , and . If the triangle is rotated through an angle of 28 clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places. , Let the vector describe a triangle with vertices at , , and . If the triangle is rotated through an angle of 28 clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places. , and Let the vector describe a triangle with vertices at , , and . If the triangle is rotated through an angle of 28 clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places. . If the triangle Let the vector describe a triangle with vertices at , , and . If the triangle is rotated through an angle of 28 clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places. is rotated through an angle of 28 Let the vector describe a triangle with vertices at , , and . If the triangle is rotated through an angle of 28 clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places. clockwise about the origin, what is the resulting vector? Round each entry to 2 decimal places.

(Short Answer)
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Question 38

The inverse of a matrix The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? , denoted by The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? , is such that if The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? , then The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? . For a matrix The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? , the inverse The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? is given by The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? , where The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? . The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? is undefined if D = 0. Let The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? . Does The inverse of a matrix , denoted by , is such that if , then . For a matrix , the inverse is given by , where . is undefined if D = 0. Let . Does ? ?

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Question 39

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