**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: **

- A
- B
- C
- D
- E