Worksheet: Rotation Matrices

Q1:

Find, with respect to the standard basis, the matrix which rotates every vector in counterclockwise about the origin through an angle of .

• A
• B
• C
• D
• E

Q2:

Find, with respect to the standard basis, the matrix which rotates every vector in counterclockwise about the origin through an angle of .

• A
• B
• C
• D
• E

Q3:

Find, with respect to the standard basis, the matrix which rotates every vector in counterclockwise about the origin through an angle of .

• A
• B
• C
• D
• E

Q4:

Describe the geometric effect of the transformation produced by the matrix .

• Aa rotation through an angle of
• Ba rotation through an angle of
• Ca rotation through an angle of
• Da rotation through an angle of
• Ea rotation through an angle of

Q5:

Find the matrix for the linear transformation that rotates every vector in through an angle of .

• A
• B
• C
• D
• E

Q6:

Consider the linear map , which acts by rotating a vector counterclockwise around the origin. Which of the following is the matrix of the linear transformation?

• A
• B
• C
• D
• E

Q7:

Find the matrix for the linear transformation which rotates every vector in through an angle of .

• A
• B
• C
• D
• E

Q8:

Find the matrix for the linear transformation which rotates every vector in through an angle of .

• A
• B
• C
• D
• E

Q9:

A rotation with center the origin sends the vector to . Find the matrix representation of this rotation.

• A
• B
• C
• D
• E

Q10:

Consider the linear transformation , which rotates each vector 90 degrees counterclockwise about the positive -axis then 45 degrees counterclockwise about the positive -axis. Find the matrix representation of in the standard basis.

• A
• B
• C
• D

Q11:

Consider the linear transformation , which rotates each vector 45 degrees counterclockwise about the positive -axis then 90 degrees counterclockwise about the positive -axis. Find in the standard basis.

• A
• B
• C
• D

Q12:

Find the matrix for the linear transformation which rotates every vector in through an angle of .

• A
• B
• C
• D
• E

Q13:

Find the matrix for the linear transformation which rotates every vector in through an angle of .

• A
• B
• C
• D
• E

Q14:

Let be the matrix of the transformation which rotates all vectors in through an angle of , where . For which values of does have a real eigenvalue?

• A and
• B and
• C and
• D and
• E and

Q15:

Find the matrix for the linear transformation that rotates every vector in through an angle of .

• A
• B
• C
• D
• E

Q16:

Find, with respect to the standard basis, the matrix which rotates every vector in counterclockwise about the origin through an angle of .

• A
• B
• C
• D
• E