| |
| |
1. |
A quantity with only magnitude is called a _____. |
| |
|
A. |
resultant |
B. |
matrix |
| |
|
C. |
scalar |
D. |
vector |
| |
|
Hint |
|
| |
2. |
The magnitude of the zero vector is _____. |
| |
|
A. |
1 |
B. |
any positive number except 1 |
| |
|
C. |
0 |
D. |
any negative number |
| |
|
Hint |
|
| |
3. |
A vector that has a magnitude of one is called a _____. |
| |
|
A. |
unit vector |
B. |
resultant |
| |
|
C. |
scalar |
D. |
magnitude |
| |
|
Hint |
|
| |
4. |
Find the magnitude of  for T(4, 0, -6) and M(5, -1, 0). |
| |
|
A. |
6 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
5. |
Find the inner product of  and  if  and  . |
| |
|
A. |
12 |
B. |
20 |
| |
|
C. |
-20 |
D. |
-12 |
| |
|
Hint |
|
| |
6. |
The cross product of two vectors is _______. |
| |
|
A. |
parallel to both vectors |
B. |
perpendicular to both vectors |
| |
|
C. |
a dot product |
D. |
not a vector |
| |
|
Hint |
|
| |
7. |
Find the initial horizontal velocity and vertical velocity of a stone kicked with an initial velocity of 15 feet per second at an angle of 42° with the ground. |
| |
|
A. |
about 11 ft/s, about 10 ft/s |
B. |
about 14 ft/s, about 12 ft/s |
| |
|
C. |
about 10 ft/s, about 22 ft/s |
D. |
about 11 ft/s, about 13 ft/s |
| |
|
Hint |
|
| |
8. |
A football player kicks a football with an initial velocity of 25 yards per second at an angle of 77° to the horizontal. What is the hang time, the elapsed time between the moment the ball is kicked and the time it hits the ground? |
| |
|
A. |
about 4.8 seconds |
B. |
about 4.4 seconds |
| |
|
C. |
about 4.2 seconds |
D. |
about 4.6 seconds |
| |
|
Hint |
|
| |
9. |
A transformation in three-dimensional space is represented by  . Which matrix represents this transformation? |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
10. |
If  , then  = _______. |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
11. |
Write  as the sum of unit vectors for U(4, 3, -8) and V(-5, -4, -2). |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
12. |
In physics, you can determine how much force with which an object is sliding down a frictionless incline by adding the gravitational force vector and the ''normal force'' vector. The normal force vector is always directed up out of the incline perpendicular to it (90° more than the measure of the incline). The magnitude m of the normal force can be calculated by m = f cos  , where f is the gravitational force and is the angle measure of the incline. If a gravitational force (always straight down) of 50 N is being exerted on an object on a 25° incline, what is the magnitude of the force with which it is sliding down the incline? |
| |
|
 |
| |
|
A. |
93.1 N |
B. |
21.1 N |
| |
|
C. |
50 N |
D. |
45.3 N |
| |
|
Hint |
|
| |
13. |
If José pushes a cart horizontally, exerting a horizontal force of 0.5 N up a 45° incline so that the cart moves 3 m, how much work has José done on the cart? A joule (J) is the SI unit for work or energy. 1 J = 1 N · 1 m |
| |
|
A. |
 J |
B. |
 J |
| |
|
C. |
 J |
D. |
 J |
| |
|
Hint |
|
| |
14. |
Write the parametric equations for the line passing through P(3, -4) and parallel to  . |
| |
|
A. |
x = 1 + 3t and y = 9 – 4t |
B. |
x = 3 + t and y = 4 – 9t |
| |
|
C. |
x = 3t + 1 and y = 4t - 9 |
D. |
x = t + 3 and y = 9t - 4 |
| |
|
Hint |
|
| |
15. |
Write parametric equations for 2x + 4y = 11. |
| |
|
A. |
x = 2t - 11 and y = 4t - 11 |
| |
|
B. |
x =  and y =  |
| |
|
C. |
x = t and y = |
| |
|
D. |
x = t and y = |
| |
|
Hint |
|
| |
16. |
If a rectangular prism represented by the vertex matrix below is translated using the vector  , find the vertex matrix for the translated image.
 |
| |
|
A. |
 |
| |
|
B. |
 |
| |
|
C. |
 |
| |
|
D. |
 |
| |
|
Hint |
|
|
|