What is the primary purpose of a rotation transformation in R2?

Understanding Rotation Transformations

Interactive Video
•
Mathematics, Physics
•
9th - 12th Grade
•
Hard

Sophia Harris
FREE Resource
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10 questions
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1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
To reflect vectors
To scale vectors
To translate vectors
To rotate vectors by a specific angle
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which of the following is a condition for a transformation to be linear?
The transformation of a vector difference equals the difference of the transformations
The transformation of a vector product equals the product of the transformations
The transformation of a vector sum equals the sum of the transformations
The transformation of a vector quotient equals the quotient of the transformations
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in constructing a rotation matrix?
Using a diagonal matrix
Starting with a zero matrix
Using the inverse matrix
Starting with the identity matrix
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the identity matrix in constructing a rotation matrix?
It provides the basis vectors for the transformation
It scales the vectors
It reflects the vectors
It translates the vectors
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How is the new x-coordinate of a rotated vector determined?
By using the sine of the angle
By using the tangent of the angle
By using the cosine of the angle
By using the cotangent of the angle
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the y-coordinate of the rotated basis vector e2?
Negative sine of theta
Sine of theta
Negative cosine of theta
Cosine of theta
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the role of trigonometry in deriving the rotation matrix?
To find the translation distances
To determine the scaling factors
To calculate the new coordinates of the rotated vectors
To reflect the vectors
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