| |
| |
1. |
A quantity with only magnitude is called a _____. |
| |
|
A. |
matrix |
B. |
resultant |
| |
|
C. |
vector |
D. |
scalar |
| |
|
Hint |
|
| |
2. |
A ship leaving port sails for 100 miles in a direction 40° north of due east. Find the magnitude of the vertical and horizontal components. |
| |
|
A. |
about 50 miles; about 87 miles |
B. |
about 87 miles; about 50 miles |
| |
|
C. |
about 77 miles; about 84 miles |
D. |
about 64 miles; about 77 miles |
| |
|
Hint |
|
| |
3. |
Write the ordered pair that represents the vector from X(-4, 7) to Y(3, -4). |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
4. |
Let . Find . |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
5. |
Find the magnitude of for T(4, 0, -6) and M(5, -1, 0). |
| |
|
A. |
6 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
6. |
Find the inner product of and if and . |
| |
|
A. |
14 |
B. |
-12 |
| |
|
C. |
-14 |
D. |
-8 |
| |
|
Hint |
|
| |
7. |
What is the magnitude of the resultant of a 100-newton force along the x-axis and a 150-newton force at an angle of 40° to each other? |
| |
|
A. |
125 N |
B. |
235.54 N |
| |
|
C. |
180.28 N |
D. |
162.99 N |
| |
|
Hint |
|
| |
8. |
Find the parametric equations for a line parallel to and passing through the point at (-3, -5). |
| |
|
A. |
x = -4 - 3t and y = -2 - 5t |
B. |
x = -4 + 3t and y = 2 + 5t |
| |
|
C. |
x = -3 + 4t and y = -5 - 2t |
D. |
x = 4 - 3t and y = -2 + 5t |
| |
|
Hint |
|
| |
9. |
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 |
|
| |
10. |
Write as the sum of unit vectors for U(4, 3, -8) and V(-5, -4, -2). |
| |
|
A. |
 |
B. |
 |
| |
|
C. |
 |
D. |
 |
| |
|
Hint |
|
| |
11. |
Find if and . |
| |
|
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. |
21.1 N |
B. |
93.1 N |
| |
|
C. |
45.3 N |
D. |
50 N |
| |
|
Hint |
|
| |
13. |
Write an equation in slope-intercept form of the line whose parametric equations are x = 3t - 4 and y = -t + 8. |
| |
|
A. |
y = 3x - 4 |
B. |
y = -3t + 12 |
| |
|
C. |
 |
D. |
y = 8 - x |
| |
|
Hint |
|
| |
14. |
Karla is in a contest to see who can hit a baseball the farthest. If she hits a ball with an initial velocity of 94.5 ft/s at an angle of 42° with the horizontal, how far will the ball travel before it hits the ground? |
| |
|
A. |
277 ft |
B. |
250 ft |
| |
|
C. |
395 ft |
D. |
139 ft |
| |
|
Hint |
|
| |
15. |
If a quarterback throws a 30-yard pass to his receiver with an initial velocity of 21 yards per second at an angle of 15 with the horizontal, how long is the ball in the air? |
| |
|
A. |
5.52 s |
B. |
0.68 s |
| |
|
C. |
1.43 s |
D. |
1.48 s |
| |
|
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 |
|
|
|