1.12 Game0130r: review  (Page 2/2)

• The angle is 0 degrees to 360 degrees measured as a counter-clockwise rotation from the positive x axis.
• The angle is 0 degrees to +180 degrees measured as a counter-clockwise rotation from the positive x axis, or is 0 degrees to -180 degrees measured as a clockwise rotation fromthe positive x axis.

Kjell, Chapter 5

What is the direction of the vector represented by (5,-5)T

• A. 0 degrees
• B. 45 degrees
• C. 315 degrees
• D.-45 degrees

Answer 18

Question 19

True or False: The formula for the direction of a 2D vector is:

angle of (x, y)T = arc tan( y/x )

Answer 19

Question 20

What is the direction of the vector represented by (5,-5)T

• A. 45 degrees
• B. 135 degrees
• C. -45 degrees
• D. -135 degrees

Answer 20

Question 21

What is the direction of the vector represented by (-5,-5)T

• A. 45 degrees
• B. 135 degrees
• C. -45 degrees
• D. -135 degrees

Answer 21

Question 22

A vector has a length of 4 and an orientation of 150 degrees. Which of the following transpose matrices properly describes the vector?

• A. (-3.464,2.0)T
• B. (-2.0,3.464)T

Answer 22

Question 23

True or False: 2*pi radians = 180 degrees

where the asterisk indicates multiplication and pi is the constant that begins with 3.14159

Answer 23

What is the meaning of the following two images?

These images were inserted here simply to insert some space between the questions and the answers to keep them from being visible on the screen at thesame time.

This image was also inserted for the purpose of inserting space between the questions and the answers.

Answers

Answer 23

False. There are 2*pi radians in a full circle, so

2*pi radians = 360 degrees

Back to Question 23

Answer 22

A. (-3.464,2.0)T

Kjell, Chapter 5

Back to Question 22

Answer 21

D. -135 degrees

Kjell, Chapter 5

Back to Question 21

Answer 20

C. -45 degrees

Kjell, Chapter 5

Back to Question 20

Answer 19

True. Arc tan( z ) means "find the angle that has a tangent of z." When you do this with a calculator, remember that the answer may be in radians or in degrees. Some calculators give you the option of using use either format.

Kjell, Chapter 5

Back to Question 19

Answer 18

C. 315 degrees, or

D.-45 degrees

depending on the convention in use.

Kjell, Chapter 5

Back to Question 18

Answer 17

True

Kjell, Chapter 5

Back to Question 17

Answer 16

False. If v is a vector, then -v is a vector pointing in the opposite direction.

Kjell, Chapter 4.

Back to Question 16

Answer 15

False. It is possible for the sum of the squared elements to be equal without the elements themselves being equal. In that case, the lengths are the same but the directions are not the same.

Kjell, Chapter 4.

Back to Question 15

Answer 14

True. Since corresponding elements must be equal, so corresponding squares must be equal, so the sum must be equal, so the length must be equal.

Kjell, Chapter 4

Back to Question 14

Answer 13

False. The length property of a vector must be zero or positive. It cannot be negative.

Kjell, Chapter 4.

Back to Question 13

Answer 12

True

Kjell, Chapter 4

Back to Question 12

Answer 11

C. 6

Kjell, Chapter 4

Back to Question 11

Answer 10

False. The correct statement follows where |(x,y,z)T| represents a three-dimensional vector:

|(x,y,z)T| = sqrt(x^2 + y^2 + z^2)

Kjell, Chapter 4

Back to Question 10

Answer 9

True

Kjell, Chapter 4

Back to Question 9

Answer 8

False. The following statement is true where the left angle bracket followed by the equal sign indicates "less than orequal." This is known as the "triangle inequality."

|u + v| is less than or equal |u| + |v|

(Note that there is a problem with displaying the left angle bracket using my xhtml to cnxml converter program. That is why it is spelled out in theabove statement.)

Kjell, Chapter 4

Back to Question 8

Answer 7

C. 5

Kjell, Chapter 4

Back to Question 7

Answer 6

C. 5

Kjell, Chapter 4

Back to Question 6

Answer 5

C. 10

Kjell, Chapter 4

Back to Question 5

Answer 4

C. 4

The length of the vector is 4 units.

Kjell, Chapter 4

Back to Question 4

Answer 3

False. The correct statement is:

When a 2D vector is aligned with the y axis, the column matrix that represents it has a non-zero value in the second element, and zero for the firstelement.

Kjell, Chapter 4

Back to Question 3

Answer 2

True. as in (3,0)T

Kjell, Chapter 4

Back to Question 2

Answer 1

B. 3

The length of the vector is 3 units.

Kjell, Chapter 4

Back to Question 1

Miscellaneous

This section contains a variety of miscellaneous information.

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