##### Exercise1

For each of the following geometric operations in the plane, find a $$2\times 2$$ matrix that defines the matrix transformation performing the operation.

1. Rotates vectors by $$180^\circ\text{.}$$

2. Reflects vectors in the vertical axis.

3. Reflects vectors in the line $$y=-x\text{.}$$

4. Rotates vectors counterclockwise by $$60^\circ\text{.}$$

5. First rotates vectors counterclockwise by $$60^\circ$$ and then reflects in the line $$y=x\text{.}$$

in-context