Unit Test 8
Find the rectangular coordinates of the point (4, pi/3)
A.
Given T(3,-5,6) and M(-1,1,2) find the ordered triple that represents TM
A.
Find the rectangular coordinates of the point (-4, pi/3)
A. (-2,-2 square root 3)
Determine two pairs of polar coordinates for (4,4) when
A. (4 square root 2, 45 degrees) (-4 square root 2,225.)
Find the magnitude of WX for W(6,-3,6) and X(6,3,4)
A. 2 square root 10
Determine the projection of w onto u 1104-11-03-00-00_v2_files/i0030002.jpg
A. 6.2i-4.2 j
The angle between a 180-pound force F and AB = 5i + 2j is 30 degrees. Find the work done by F in moving and object from A to B.
A. 839 foot-pounds
Write the polar equation theta = pi/3 in rectangular form.
D.
Determine two pairs of polar coordinates for (3,-3) when
B) (3 square root 2, 315 degrees) (-3 square root 2, 135 degrees)
Which is the graph of r = 6 cos theta
B.
Triangle ABC is shown below. mc010-1.jpg Which point is the coordinate of the image of A under the transformation mc010-2.jpg?
B. (-4, 2)
Find an equation equivalent to 2x + 3y = 6 in polar coordinates.
C.
Determine two pairs of polar coordinates for (-3,0) when
a. (3,180°), (-3,0°)
Justine reflects a vector v across the y-axis. Simonne reflects a vector v by rotating it 90° counterclockwise about the origin. Which of the following vectors has the same image for Justin and Simonne?
A.
Suppose that during a storm the force of the wind blowing against a skyscraper can be expressed by the vector (132,3454,0), where each measure in the ordered triple represents the force in newtons. what is the magnitude of this force?
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.
Given T(-5,8,3) and M(-2,--1,-6)
B. (3,-9,-9);3 square root 19.
Given R(3,7,-1), S(10,-4,0) find an ordered triple that represents RS and find the magnitude of RS
B. (7,-11,1), 3 square root 19
Which angle of rotation is determined by the matrix below?
B. 60°
Use the dot product to find |v| when v = -6i.
d. 6
Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu U=(-9,3), v(-9,-3)
A.
The diagram below shows rectangle ABCD. Which points are in the image of rectangle ABCD under the transformation: mc013-2.jpg?
A. A'(3,9); ect
Which is the graph of the polar equation r = 3 sin2 theta
B.
Given T(2,5,4) and M(3,1,0) find the ordered triple that represents TM Then find the magnitude of TM
C.
What is the magnitude of the resultant of z-y?
D. 5 square root 2
Find an equation equivalent to r = 5/1+ cos theta in rectangular coordinates.
D. y^2=25-10x
Find the angle between u =square root 5i-8j and v = square root 5i+ j. Round to the nearest tenth of a degree
b. 98.5 degrees
The diagram below shows vector v. mc009-1.jpg Given transformation matrix mc009-2.jpg, which diagram shows the application of T to v?
A.
Find an ordered triple to represent u in u=1/2 v - w+ 2z if v= (4,-3,5)
D (6,-7 1/2, 11 1/2)
Find a . b if a = 3i + 8j and b = -0.5i - 4j.
b. -33.5
Find a . b if a = 10i + 4j and b = 3i + 4j.
c. 46
Determine whether the vectors u and v are parallel, orthogonal, or neither. u=(9,0), v=(0,-9)
c. Orthogonal
Which angle of rotation is determined by the matrix below?
c.225°
Which is the graph of the polar equation r = 4 cos3 theta
B.
Which transformation matrix would result in a 270° counterclockwise rotation about the origin?
B.
Which transformation matrix would result in a 300° counterclockwise rotation about the origin?
B.
Find an ordered triple to represent a in the equation a=2g-5f if f=(1,-3,-8) and g=(3,9,-1)
B. (1,33,38)
Given U=(1,-1,3) and V(-4,5,3) find an ordered triple that represents 3u-2v
B. (11,-13,3)
Find an equation equivalent to r = 1 + 2 sin theta in rectangular coordinates.
C.
Triangle ABC is shown below. mc011-1.jpg Which point is the coordinate of the image of A under the transformation
C. (4, 2)
Find an ordered triple to represent a in the equation a=3f+g if f=(1,-3,-8) and g(3,9,-1)
C. (6,0,-25)
Use the dot product to find |v| when v = (-8,2)
C. 2 square root 17
Find the magnitude of WX for W(-2,-8,-3) and X(1,4,-1)
C. Square root 29
Which sequence of steps would transform v to v'?
C. reflect across the line y = -x; rotate 90° counterclockwise about the origin
Use the dot product to find |v| when v = (-2,-1)
C. square root 5.
Find an ordered triple to represent u in u=0.75v+0.25w if v=(4,-3,5), w=(2,6,-1), and z=(3,0,4)
C.(3.5,-0.75,3.5)
Find an equation equivalent to x2 - y2 = 4 in polar coordinates.
D.
Given R(-2,5,8), S(3,9,-3) find an ordered triple that represents RS and find the magnitude of RS
D.
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?
D.
The diagram below shows vector v. Given transformation matrix mc008-2.jpg, which diagram shows the application of T to v?
D.
Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu u=(-8,-8),v=(-1,2)
D.
A constant force of F = 47i + 30j moves an object along a vector D = 13i - 8j, where units are in pounds and feet. Find the work done.
b. 371 foot-pounds
Find an equation equivalent to r= 7 csc theta in rectangular coordinates and describe the graph of the equation.
b. y=7; straight horizontal line
The transformation T = mc018-1.jpg is applied the figure below. What type of transformation of triangle ABC was applied by T?
c. reflect across the line y = -x
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.
d. 3.66 mi
What is the minimum force required to prevent a ball weighing 22.6 lb from rolling down a ramp which is inclined at 39.0 degrees with the horizontal?
d. 14.2 lb
Find the work done lifting a 290-pound weight 28 feet in the air.
d. 8,120 foot-pounds
Find an equation equivalent to x2 - y2 = 4 in polar coordinates.
d. r2 cos2 theta = 4