FP1 Rotation matrices?

I am absolutely lost on rotation matrices, could someone explain how to find out what the matrix would be based on criteria like:
- Rotation by 135* clockwise
- Rotation by 135* ACW
- Rotation by 45* CW
- Rotation by 45* ACW
(about origin (0,0))
Could you please explain the line of thought when approaching the questions?

Yep I can do others such as reflection y= -x etc but I just can't understand rotation matrices

Rotation transformation in $\mathbb{R}^2$ has a matrix of the form $\displaystyle \begin{pmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{pmatrix}$ where $\theta$ is measured from the positive x-axis anticlockwise. It is in your formula booklet (I think...)

So try and deduce the matrices for your examples using this info.

I've seen that but I have no idea how to use it, could you do anticlockwise 135* as an example? Thanks

I've seen that but I have no idea how to use it, could you do anticlockwise 135* as an example? Thanks

I am absolutely lost on rotation matrices, could someone explain how to find out what the matrix would be based on criteria like:
- Rotation by 135* clockwise
- Rotation by 135* ACW
- Rotation by 45* CW
- Rotation by 45* ACW
(about origin (0,0))
Could you please explain the line of thought when approaching the questions?

Do you have to work out exact values to get the mark or can you leave it in trig form

You'll have to equate an element in the matrix to a trig function and then resolve for theta. Then using that theta figure out what actually happens to the line and say something like "A rotation about the origin by 45* anticlockwise"