Vectors and Polar Coordinates

B
Which transformation matrix would result in a 270° counterclockwise rotation about the origin?
reflect across the y-axis; rotate 180° counterclockwise about the origin
The graph below shows the transformation from triangle 1 to triangle 2.

mc025-1.jpg

Which sequence of steps would transform triangle 1 to triangle 2?

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rotate 90° counterclockwise about the origin
The transformation T = mc017-1.jpg is applied the figure below.

mc017-2.jpg

Which transformation is applied to the figure?

D
The diagram below shows vector v.

mc008-1.jpg

Given transformation matrix mc008-2.jpg, which diagram shows the application of T to v?

NOT B
Given the vector mc016-1.jpg and the transformation matrix mc016-2.jpg, which vector is the image after applying the transformation to mc016-3.jpg?
NOT D
Which transformation matrix would result in a 300° counterclockwise rotation about the origin?
NOT C
Which image is a reflection over the line y = x of triangle 1?

mc015-1.jpg

NOT D
Which angle of rotation is determined by the matrix below?

mc020-1.jpg

NOT B
Hugo reflects a vector v across the line y = -x. Nemo rotates a vector v 180° counterclockwise about the origin. Which of the following vectors would have the same image for Hugo and Nemo?
(-4, 2)
Triangle ABC is shown below.

mc010-1.jpg

Which point is the coordinate of the image of A under the transformation mc010-2.jpg?

NOT B
Use the dot product to find 649-11-03-00-00_files/i0170000.jpg when v = 649-11-03-00-00_files/i0170001.jpg.
a.
649-11-03-00-00_files/i0170002.jpg
c.
649-11-03-00-00_files/i0170003.jpg
b.
10
d.
-6

Please select the best answer from the choices provided

C
Find a 649-11-03-00-00_files/i0070000.jpg b if a = 649-11-03-00-00_files/i0070001.jpg and b = 649-11-03-00-00_files/i0070002.jpg.
a.
-30
c.
-34
b.
649-11-03-00-00_files/i0070003.jpg
d.
649-11-03-00-00_files/i0070004.jpg

Please select the best answer from the choices provided

NOT A
Find the angle between u = 649-11-03-00-00_files/i0150000.jpg and v = 649-11-03-00-00_files/i0150001.jpg. Round to the nearest tenth of a degree.
a.
65.9649-11-03-00-00_files/i0150002.jpg
c.
90.4649-11-03-00-00_files/i0150003.jpg
b.
98.5649-11-03-00-00_files/i0150004.jpg
d.
33.3649-11-03-00-00_files/i0150005.jpg

Please select the best answer from the choices provided

NOT D
Use the dot product to find 649-11-03-00-00_files/i0200000.jpg when v = 649-11-03-00-00_files/i0200001.jpg.
a.
-1
c.
649-11-03-00-00_files/i0200002.jpg
b.
-3
d.
649-11-03-00-00_files/i0200003.jpg

Please select the best answer from the choices provided

A
Find the work done lifting a 290-pound weight 28 feet in the air.
a.
4,582 foot-pounds
c.
No work is done
b.
6,132 foot-pounds
d.
8,120 foot-pounds

Please select the best answer from the choices provided

C
Find a 649-11-03-00-00_files/i0080000.jpg b if a = 10i + 4j and b = 3i + 4j.
a.
649-11-03-00-00_files/i0080001.jpg
c.
46
b.
-14
d.
649-11-03-00-00_files/i0080002.jpg

Please select the best answer from the choices provided

NOT D
Find a 649-11-03-00-00_files/i0090000.jpg b if a = 3i + 8j and b = -0.5i – 4j.
a.
649-11-03-00-00_files/i0090001.jpg
c.
649-11-03-00-00_files/i0090002.jpg
b.
-33.5
d.
-30.5

Please select the best answer from the choices provided

NOT C
Use the dot product to find 649-11-03-00-00_files/i0210000.jpg when v = -6i.
a.
0
c.
36
b.
-6
d.
6

Please select the best answer from the choices provided

NOT C
What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0649-11-03-00-00_files/i0260000.jpg with the horizontal?
a.
7.1 lb
c.
17.6 lb
b.
8.8 lb
d.
14.4 lb

Please select the best answer from the choices provided

A
The angle between a 180-pound force F and 649-11-03-00-00_files/i0230000.jpg = 5i + 2j is 30649-11-03-00-00_files/i0230001.jpg. Find the work done by F in moving and object from A to B.
a.
649-11-03-00-00_files/i0230002.jpg 839 foot-pounds
c.
649-11-03-00-00_files/i0230003.jpg 1091.19 foot-pounds
b.
649-11-03-00-00_files/i0230004.jpg 484.66 foot-pounds
d.
649-11-03-00-00_files/i0230005.jpg 969.33 foot-pounds

Please select the best answer from the choices provided

C
Use the dot product to find 649-11-03-00-00_files/i0170000.jpg when v = 649-11-03-00-00_files/i0170001.jpg.
a.
649-11-03-00-00_files/i0170002.jpg
c.
649-11-03-00-00_files/i0170003.jpg
b.
10
d.
-6

Please select the best answer from the choices provided

C
Find a 649-11-03-00-00_files/i0070000.jpg b if a = 649-11-03-00-00_files/i0070001.jpg and b = 649-11-03-00-00_files/i0070002.jpg.
a.
-30
c.
-34
b.
649-11-03-00-00_files/i0070003.jpg
d.
649-11-03-00-00_files/i0070004.jpg

Please select the best answer from the choices provided

A
The angle between a 180-pound force F and 649-11-03-00-00_files/i0230000.jpg = 5i + 2j is 30649-11-03-00-00_files/i0230001.jpg. Find the work done by F in moving and object from A to B.
a.
649-11-03-00-00_files/i0230002.jpg 839 foot-pounds
c.
649-11-03-00-00_files/i0230003.jpg 1091.19 foot-pounds
b.
649-11-03-00-00_files/i0230004.jpg 484.66 foot-pounds
d.
649-11-03-00-00_files/i0230005.jpg 969.33 foot-pounds

Please select the best answer from the choices provided

A
The angle between a 180-pound force F and 649-11-03-00-00_files/i0230000.jpg = 5i + 2j is 30649-11-03-00-00_files/i0230001.jpg. Find the work done by F in moving and object from A to B.
a.
649-11-03-00-00_files/i0230002.jpg 839 foot-pounds
c.
649-11-03-00-00_files/i0230003.jpg 1091.19 foot-pounds
b.
649-11-03-00-00_files/i0230004.jpg 484.66 foot-pounds
d.
649-11-03-00-00_files/i0230005.jpg 969.33 foot-pounds

Please select the best answer from the choices provided

C
Use the dot product to find 649-11-03-00-00_files/i0200000.jpg when v = 649-11-03-00-00_files/i0200001.jpg.
a.
-1
c.
649-11-03-00-00_files/i0200002.jpg
b.
-3
d.
649-11-03-00-00_files/i0200003.jpg

Please select the best answer from the choices provided

D
Use the dot product to find 649-11-03-00-00_files/i0210000.jpg when v = -6i.
a.
0
c.
36
b.
-6
d.
6

Please select the best answer from the choices provided

C
Find a 649-11-03-00-00_files/i0080000.jpg b if a = 10i + 4j and b = 3i + 4j.
a.
649-11-03-00-00_files/i0080001.jpg
c.
46
b.
-14
d.
649-11-03-00-00_files/i0080002.jpg

Please select the best answer from the choices provided

D
Find the work done lifting a 290-pound weight 28 feet in the air.
a.
4,582 foot-pounds
c.
No work is done
b.
6,132 foot-pounds
d.
8,120 foot-pounds

Please select the best answer from the choices provided

B
Find a 649-11-03-00-00_files/i0090000.jpg b if a = 3i + 8j and b = -0.5i – 4j.
a.
649-11-03-00-00_files/i0090001.jpg
c.
649-11-03-00-00_files/i0090002.jpg
b.
-33.5
d.
-30.5

Please select the best answer from the choices provided

B
Find a 649-11-03-00-00_files/i0090000.jpg b if a = 3i + 8j and b = -0.5i – 4j.
a.
649-11-03-00-00_files/i0090001.jpg
c.
649-11-03-00-00_files/i0090002.jpg
b.
-33.5
d.
-30.5

Please select the best answer from the choices provided

C
Find a 649-11-03-00-00_files/i0070000.jpg b if a = 649-11-03-00-00_files/i0070001.jpg and b = 649-11-03-00-00_files/i0070002.jpg.
a.
-30
c.
-34
b.
649-11-03-00-00_files/i0070003.jpg
d.
649-11-03-00-00_files/i0070004.jpg

Please select the best answer from the choices provided

D
What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0649-11-03-00-00_files/i0260000.jpg with the horizontal?
a.
7.1 lb
c.
17.6 lb
b.
8.8 lb
d.
14.4 lb

Please select the best answer from the choices provided

B
Given 649-11-04-00-00_files/i0020000.jpg and 649-11-04-00-00_files/i0020001.jpg find an ordered triple that represents 649-11-04-00-00_files/i0020002.jpg.
a.
649-11-04-00-00_files/i0020003.jpg
c.
649-11-04-00-00_files/i0020004.jpg
b.
649-11-04-00-00_files/i0020005.jpg
d.
649-11-04-00-00_files/i0020006.jpg

Please select the best answer from the choices provided

C
Find the magnitude of 649-11-04-00-00_files/i0050000.jpg for 649-11-04-00-00_files/i0050001.jpg and 649-11-04-00-00_files/i0050002.jpg.
a.
649-11-04-00-00_files/i0050003.jpg
c.
649-11-04-00-00_files/i0050004.jpg
b.
649-11-04-00-00_files/i0050005.jpg
d.
649-11-04-00-00_files/i0050006.jpg

Please select the best answer from the choices provided

C
Find an ordered triple to represent 649-11-04-00-00_files/i0220000.jpg in 649-11-04-00-00_files/i0220001.jpg if 649-11-04-00-00_files/i0220002.jpg, 649-11-04-00-00_files/i0220003.jpg, and 649-11-04-00-00_files/i0220004.jpg.
a.
649-11-04-00-00_files/i0220005.jpg
c.
649-11-04-00-00_files/i0220006.jpg
b.
649-11-04-00-00_files/i0220007.jpg
d.
649-11-04-00-00_files/i0220008.jpg

Please select the best answer from the choices provided

A
Given 649-11-04-00-00_files/i0160000.jpg and 649-11-04-00-00_files/i0160001.jpg find the ordered triple that represents 649-11-04-00-00_files/i0160002.jpg. Then find the magnitude of 649-11-04-00-00_files/i0160003.jpg.
a.
649-11-04-00-00_files/i0160004.jpg; 649-11-04-00-00_files/i0160005.jpg
c.
649-11-04-00-00_files/i0160006.jpg; 649-11-04-00-00_files/i0160007.jpg
b.
649-11-04-00-00_files/i0160008.jpg; 649-11-04-00-00_files/i0160009.jpg
d.
649-11-04-00-00_files/i0160010.jpg; 649-11-04-00-00_files/i0160011.jpg

Please select the best answer from the choices provided

B
Find the magnitude of 649-11-04-00-00_files/i0040000.jpg for 649-11-04-00-00_files/i0040001.jpg and 649-11-04-00-00_files/i0040002.jpg.
a.
649-11-04-00-00_files/i0040003.jpg
c.
649-11-04-00-00_files/i0040004.jpg
b.
649-11-04-00-00_files/i0040005.jpg
d.
649-11-04-00-00_files/i0040006.jpg

Please select the best answer from the choices provided

C
Given 649-11-04-00-00_files/i0150000.jpg and 649-11-04-00-00_files/i0150001.jpg find the ordered triple that represents 649-11-04-00-00_files/i0150002.jpg. Then find the magnitude of 649-11-04-00-00_files/i0150003.jpg.
a.
649-11-04-00-00_files/i0150004.jpg; 649-11-04-00-00_files/i0150005.jpg
c.
649-11-04-00-00_files/i0150006.jpg; 649-11-04-00-00_files/i0150007.jpg
b.
649-11-04-00-00_files/i0150008.jpg; 649-11-04-00-00_files/i0150009.jpg
d.
649-11-04-00-00_files/i0150010.jpg; 649-11-04-00-00_files/i0150011.jpg

Please select the best answer from the choices provided

A
Find the magnitude of 649-11-04-00-00_files/i0060000.jpg for 649-11-04-00-00_files/i0060001.jpg and 649-11-04-00-00_files/i0060002.jpg.
a.
649-11-04-00-00_files/i0060003.jpg
c.
649-11-04-00-00_files/i0060004.jpg
b.
649-11-04-00-00_files/i0060005.jpg
d.
649-11-04-00-00_files/i0060006.jpg

Please select the best answer from the choices provided

C
Find an ordered triple to represent 649-11-04-00-00_files/i0090000.jpg in the equation 649-11-04-00-00_files/i0090001.jpg if 649-11-04-00-00_files/i0090002.jpg and 649-11-04-00-00_files/i0090003.jpg.
a.
649-11-04-00-00_files/i0090004.jpg
c.
649-11-04-00-00_files/i0090005.jpg
b.
649-11-04-00-00_files/i0090006.jpg
d.
649-11-04-00-00_files/i0090007.jpg

Please select the best answer from the choices provided

B
Given 649-11-04-00-00_files/i0170000.jpg and 649-11-04-00-00_files/i0170001.jpg find the ordered triple that represents 649-11-04-00-00_files/i0170002.jpg. Then find the magnitude of 649-11-04-00-00_files/i0170003.jpg.
a.
649-11-04-00-00_files/i0170004.jpg; 649-11-04-00-00_files/i0170005.jpg
c.
649-11-04-00-00_files/i0170006.jpg; 649-11-04-00-00_files/i0170007.jpg
b.
649-11-04-00-00_files/i0170008.jpg; 649-11-04-00-00_files/i0170009.jpg
d.
649-11-04-00-00_files/i0170010.jpg; 649-11-04-00-00_files/i0170011.jpg

Please select the best answer from the choices provided

A
Suppose that during a storm the force of the wind blowing against a skyscraper can be expressed by the vector 649-11-04-00-00_files/i0130000.jpg, where each measure in the ordered triple represents the force in newtons. what is the magnitude of this force?
a.
649-11-04-00-00_files/i0130001.jpg N
c.
649-11-04-00-00_files/i0130002.jpg N
b.
649-11-04-00-00_files/i0130003.jpg N
d.
649-11-04-00-00_files/i0130004.jpg N

Please select the best answer from the choices provided

A
Plot the point 649-11-07-00-00_files/i0050000.jpg.
a.
649-11-07-00-00_files/i0050001.jpg
b.
649-11-07-00-00_files/i0050002.jpg

Please select the best answer from the choices provided

A
Find the rectangular coordinates of the point 649-11-07-00-00_files/i0030000.jpg.
a.
649-11-07-00-00_files/i0030001.jpg
c.
649-11-07-00-00_files/i0030002.jpg
b.
649-11-07-00-00_files/i0030003.jpg
d.
649-11-07-00-00_files/i0030004.jpg

Please select the best answer from the choices provided

B
Determine two pairs of polar coordinates for (3,-3) when 649-11-07-00-00_files/i0090000.jpg
a.
649-11-07-00-00_files/i0090001.jpg
c.
649-11-07-00-00_files/i0090002.jpg
b.
649-11-07-00-00_files/i0090003.jpg
d.
649-11-07-00-00_files/i0090004.jpg

Please select the best answer from the choices provided

B
Find an equation equivalent to in rectangular coordinates and describe the graph of the equation.
a.
; circle with radius 7
c.
; circle with radius 7
b.
; straight horizontal line
d.
; straight vertical line

Please select the best answer from the choices provided

D
The locations, given in polar coordinates, for two planes approaching an airport are (4 mi, 12º) and (3 mi, 73º). Find the distance between the two planes.
a.
649-11-07-00-00_files/i0260000.jpg 1.00 mi
c.
649-11-07-00-00_files/i0260001.jpg 5.00 mi
b.
649-11-07-00-00_files/i0260002.jpg 61.01 mi
d.
649-11-07-00-00_files/i0260003.jpg 3.66 mi

Please select the best answer from the choices provided

D
Find an equation equivalent to x2 – y2 = 4 in polar coordinates.
a.
cos2 649-11-07-00-00_files/i0200000.jpg – sin2 649-11-07-00-00_files/i0200001.jpg = 4r
c.
r cos2649-11-07-00-00_files/i0200002.jpg = 4
b.
cos2 649-11-07-00-00_files/i0200003.jpg – sin2 649-11-07-00-00_files/i0200004.jpg = 4
d.
r2 cos2649-11-07-00-00_files/i0200005.jpg = 4

Please select the best answer from the choices provided

C
Find an equation equivalent to 2x + 3y = 6 in polar coordinates.
a.
r (2 sin649-11-07-00-00_files/i0220000.jpg + 3 cos649-11-07-00-00_files/i0220001.jpg) = 6
c.
r (2 cos649-11-07-00-00_files/i0220002.jpg + 3 sin649-11-07-00-00_files/i0220003.jpg) = 6
b.
2 cos649-11-07-00-00_files/i0220004.jpg + 3 sin649-11-07-00-00_files/i0220005.jpg = 6r
d.
2 sin649-11-07-00-00_files/i0220006.jpg + 3 cos649-11-07-00-00_files/i0220007.jpg = 6r

Please select the best answer from the choices provided

NOT A
Find all of the polar coordinates of point P if 649-11-07-00-00_files/i0070000.jpg.
a.
649-11-07-00-00_files/i0070001.jpg or 649-11-07-00-00_files/i0070002.jpg
c.
649-11-07-00-00_files/i0070003.jpg or 649-11-07-00-00_files/i0070004.jpg
b.
649-11-07-00-00_files/i0070005.jpg or 649-11-07-00-00_files/i0070006.jpg
d.
649-11-07-00-00_files/i0070007.jpg or 649-11-07-00-00_files/i0070008.jpg

Please select the best answer from the choices provided

A
Determine two pairs of polar coordinates for (-3,0) when 649-11-07-00-00_files/i0110000.jpg
a.
(3,180°), (-3,0°)
c.
(3,0°), (-3,180°)
b.
(3,270°), (-3,90°)
d.
(3,90°), (-3,270°)

Please select the best answer from the choices provided

D
Find an equation equivalent to r = 649-11-07-00-00_files/i0160000.jpg in rectangular coordinates.
a.
649-11-07-00-00_files/i0160001.jpg
c.
649-11-07-00-00_files/i0160002.jpg
b.
649-11-07-00-00_files/i0160003.jpg
d.
649-11-07-00-00_files/i0160004.jpg

Please select the best answer from the choices provided

A
Find the rectangular coordinates of the point 649-11-07-00-00_files/i0030000.jpg.
a.
649-11-07-00-00_files/i0030001.jpg
c.
649-11-07-00-00_files/i0030002.jpg
b.
649-11-07-00-00_files/i0030003.jpg
d.
649-11-07-00-00_files/i0030004.jpg

Please select the best answer from the choices provided

A
The locations, given in polar coordinates, for two ships are (8 mi, 63º) and (8 mi, 123º). Find the distance between the two ships.
a.
649-11-07-00-00_files/i0250000.jpg 8 mi
c.
649-11-07-00-00_files/i0250001.jpg 11.31 mi
b.
649-11-07-00-00_files/i0250002.jpg 3600.00 mi
d.
649-11-07-00-00_files/i0250003.jpg 4.14 mi

Please select the best answer from the choices provided

C
Find an equation equivalent to r = 1 + 2 sin649-11-07-00-00_files/i0150000.jpg in rectangular coordinates.
a.
649-11-07-00-00_files/i0150001.jpg
c.
649-11-07-00-00_files/i0150002.jpg
b.
649-11-07-00-00_files/i0150003.jpg
d.
649-11-07-00-00_files/i0150004.jpg

Please select the best answer from the choices provided

B
Find an equation equivalent to in rectangular coordinates and describe the graph of the equation.
a.
; circle with radius 7
c.
; circle with radius 7
b.
; straight horizontal line
d.
; straight vertical line

Please select the best answer from the choices provided

D
Write the polar equation 1104-11-07-00-00_v2_files/i0030000.jpg in rectangular form.
a.
1104-11-07-00-00_v2_files/i0030001.jpg
c.
1104-11-07-00-00_v2_files/i0030002.jpg
b.
1104-11-07-00-00_v2_files/i0030003.jpg
d.
1104-11-07-00-00_v2_files/i0030004.jpg

Please select the best answer from the choices provided

A
Determine the projection of 1104-11-03-00-00_v2_files/i0030000.jpg onto 1104-11-03-00-00_v2_files/i0030001.jpg.

1104-11-03-00-00_v2_files/i0030002.jpg
a.
1104-11-03-00-00_v2_files/i0030003.jpg
c.
1104-11-03-00-00_v2_files/i0030004.jpg
b.
1104-11-03-00-00_v2_files/i0030005.jpg
d.
1104-11-03-00-00_v2_files/i0030006.jpg

Please select the best answer from the choices provided

B
What is the magnitude of the resultant of 1104-11-04-00-00_v2_files/i0030000.jpg ?

1104-11-04-00-00_v2_files/i0030001.jpg
a.
1104-11-04-00-00_v2_files/i0030002.jpg
c.
1104-11-04-00-00_v2_files/i0030003.jpg
b.
1104-11-04-00-00_v2_files/i0030004.jpg
d.
1104-11-04-00-00_v2_files/i0030005.jpg

Please select the best answer from the choices provided

C
Given 649-11-04-00-00_files/i0150000.jpg and 649-11-04-00-00_files/i0150001.jpg find the ordered triple that represents 649-11-04-00-00_files/i0150002.jpg. Then find the magnitude of 649-11-04-00-00_files/i0150003.jpg.
a.
649-11-04-00-00_files/i0150004.jpg; 649-11-04-00-00_files/i0150005.jpg
c.
649-11-04-00-00_files/i0150006.jpg; 649-11-04-00-00_files/i0150007.jpg
b.
649-11-04-00-00_files/i0150008.jpg; 649-11-04-00-00_files/i0150009.jpg
d.
649-11-04-00-00_files/i0150010.jpg; 649-11-04-00-00_files/i0150011.jpg

Please select the best answer from the choices provided

A
Determine two pairs of polar coordinates for (4,4) when 649-11-07-00-00_files/i0100000.jpg
a.
649-11-07-00-00_files/i0100001.jpg
c.
649-11-07-00-00_files/i0100002.jpg
b.
649-11-07-00-00_files/i0100003.jpg
d.
649-11-07-00-00_files/i0100004.jpg

Please select the best answer from the choices provided

C
A constant force of F = 649-11-03-00-00_files/i0040000.jpg moves an object along a vector D = 649-11-03-00-00_files/i0040001.jpg, where units are in pounds and feet. Find the work done.
a.
1082.3 foot-pounds
c.
1054 foot-pounds
b.
134 foot-pounds
d.
-134 foot-pounds

Please select the best answer from the choices provided

B
Which is the graph of r = 4 sin649-11-07-00-00_files/i0170000.jpg?
a.
649-11-07-00-00_files/i0170001.jpg
b.
649-11-07-00-00_files/i0170002.jpg

Please select the best answer from the choices provided

A
Find the work done by a force F of 21 pounds acting in the direction 649-11-03-00-00_files/i0240000.jpg in moving an object 7 feet from (0,0) to (7,0).
a.
649-11-03-00-00_files/i0240001.jpg 54.59 foot-pounds
c.
649-11-03-00-00_files/i0240002.jpg 74.09 foot-pounds
b.
649-11-03-00-00_files/i0240003.jpg 136.49 foot-pounds
d.
649-11-03-00-00_files/i0240004.jpg 294 foot-pounds

Please select the best answer from the choices provided

C
Find an equation equivalent to in rectangular coordinates and describe the graph of the equation.
a.
; circle with radius 6
c.
; straight vertical line
b.
; circle with radius 6
d.
; straight horizontal line

Please select the best answer from the choices provided

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