AnswersPrecalculusModeling with Vector Quantities

Practice Test Answers

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1
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If cap t is equal to the 2 by 2 matrix row 1, 0 1 row 2, 1 0 is a transformation matrix, which expression correctly applies cap t to v ?

A
the 2 by 2 matrix row 1, 0 1 row 2, 1 0 times the 2 by 1 column matrix row 1 negative 5 row 2 negative 4
B
the 2 by 1 column matrix row 1 negative 4 row 2 negative 5 times the 2 by 2 matrix row 1, 0 1 row 2, 1 0
C
the 2 by 1 column matrix row 1 negative 5 row 2 negative 4 times the 2 by 2 matrix row 1, 0 1 row 2, 1 0
D
the 2 by 2 matrix row 1, 0 1 row 2, 1 0 times the 2 by 1 column matrix row 1 negative 4 row 2 negative 5
2
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What is the component form and direction of the vector shown?

A
components negative 7 comma 3 and 157 degrees
B
components negative 7 comma 3 and 23 degrees
C
component 7 comma negative 3 and 23 degrees
D
components 7 comma negative 3 and 157 degrees
3

A disc spins at a rate of 6 point 4 revolutions per minute. To the nearest tenth, what is the linear velocity, in meters per minute, of a point on the disc that is 3 cm from the center of the disc?

Answer:

1.2

4

A vector in standard position has its terminal point at open paren 7 comma negative 4 close paren What is the magnitude of the vector?

A
square root of 65
B
65
C
square root of 3
D
3
5

Let vector a with components negative seven comma three and vector b with components negative two comma negative twelve , and c is equal to A plus b What is the magnitude and direction angle of vector c ?

A
magnitude of vector c is equal to 18 ; theta is equal to 135 degrees
B
magnitude of vector c is equal to 9 square root of 2 ; theta is equal to 225 degrees
C
magnitude of vector c is equal to 18 ; theta is equal to 225 degrees
D
magnitude of vector c is equal to 9 square root of 2 ; theta is equal to 135 degrees
6

Which graph represents the parametric equations x is equal to 1 minus t squared and y is equal to 2 t , where 0 is less than or equal to t comma t is less than or equal to 5 ?

A
Image with description On a coordinate plane, a curve starts at (1, 0) and curves down through (2, negative 2) to (26, negative 10).
B
Image with description On a coordinate plane, a curve starts at (1, 0) and curves up through (0, 2) to (negative 24, 10).
C
Image with description On a coordinate plane, a curve starts at (1, 0) and curves up through (2, 2) to (26, 10).
D
Image with description On a coordinate plane, a curve starts at (1, 0) and curves down through (0, negative 2) to (negative 24, negative 10).
7

A cyclist travels 5 miles in the direction cap n 30 degrees cap e , then travels 3 miles in the direction cap n 70 degrees cap e Which equation measures the cyclist’s distance, x , from the starting point?

A
x squared is equal to 5 squared plus 3 squared minus 2 5 3 cosine open paren 140 degrees close paren
B
5 squared is equal to x squared plus 3 squared minus 2 3 x cosine open paren 140 degrees close paren
C
5 squared is equal to x squared plus 3 squared minus 2 3 x cosine open paren 100 degrees close paren
D
x squared is equal to 5 squared plus 3 squared minus 2 5 3 cosine open paren 100 degrees close paren
8

Vectors vector u and vector v have magnitudes of 20 and 13 , respectively, and the angle between them is 210 degrees What is the scalar projection of vector u onto vector v ?

A
17 point 3 2
B
negative 17 point 3 2
C
11 point 2 6
D
negative 11 point 2 6
9

Let vector v with components negative thirteen comma two and vector w with components negative nine comma negative five What is vector w minus vector v ?

A
components 22 comma 3
B
components 4 comma negative 7
C
components negative 22 comma negative 23
D
components negative 4 comma 7
10

Given vectors vector u with components negative two comma one and vector v with components four comma negative two , which statement is true concerning vector u and vector v ?

A
The vectors form an obtuse angle of approximately 127 degrees .
B
The vectors form an obtuse angle of approximately 96 degrees .
C
The vectors form an obtuse angle of approximately 93 degrees .
D
The vectors point in opposite directions.
11

What is the rectangular form of the parametric equations x is equal to 6 t and y is equal to the fraction with numerator t squared and denominator 4 ?

A
y is equal to x over 144
B
y is equal to the fraction with numerator x squared and denominator 144
C
y is equal to the fraction with numerator x squared and denominator 9
D
y is equal to x over 9
12

Two planes take off from the same airport at approximately the same time. Plane A has an airspeed of 600 mph and travels in the direction cap s 20 degrees cap w Plane B has an airspeed of 450 mph and travels in the direction cap n 35 degrees cap e Which diagram represents the distance, x , between the planes?

A
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the right in quadrant 2 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the right in quadrant 4 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
B
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the right in quadrant 1 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the right in quadrant 4 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
C
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the left in quadrant 2 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the left in quadrant 3 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
D
Image with description On a coordinate plane, a vector labeled 450 miles per hour goes up and to the right in quadrant 1 and forms angle alpha = 35 degrees with the y-axis. A vector labeled 600 miles per hour goes down and to the left in quadrant 3 and forms angle beta = 20 degrees with the y-axis. Vector x goes from terminal point 600 miles per hour to terminal point 450 miles per hour.
13

A particle moves along a circular path with radius 3 centimeters. The particle has an angular velocity of 3 pi over 4 radians per second. What is the length of the arc, in centimeters, generated after 5 seconds? Round your answer to the nearest tenth.

Answer:

7.1

14

Which image is a reflection over the line y is equal to x of triangle 1?

A
Image with description On a coordinate plane,the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 4 to 4 in increments of 1. A triangle has vertices at (1, 1), (1, 4), and (3, 4). The triangle lies in the first quadrant.
B
Image with description On a coordinate plane,the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 4 to 4 in increments of 1. A triangle has vertices at (negative 4, 1), (negative 1, 1), and (negative 4, 3). The triangle lies in the second quadrant.
C
Image with description On a coordinate plane,the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 4 to 4 in increments of 1. A triangle has vertices at (negative 1, negative 4), (negative 1, negative 1), and (negative 3, negative 4). The triangle lies in the third quadrant.
D
Image with description On a coordinate plane,the x-axis ranges from negative 5 to 5 in increments of 1, and the y-axis ranges from negative 4 to 4 in increments of 1. A triangle has vertices at (4, negative 1), (1, negative 1), and (4, negative 3). The triangle lies in the fourth quadrant.

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