Finding the transformation of a matrix

[Redwaves]

I see, I didn't know that.
I guess I understand. I'll practice to make sure I understand properly.
Thank you

 

[FactChecker]

From that, the transformation seems to be an rotation of $\phi - \theta$ clockwise and then a reflection over the x axis. Is this correct?

Yes, you are correct. It can be represented by
$\begin{pmatrix} \cos(\theta) & \sin(\theta) \\ \sin(\theta) & -\cos(\theta) \end{pmatrix} = \begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix} \begin{pmatrix} \cos(-\theta) & -\sin(-\theta) \\ \sin(-\theta) & \cos(-\theta) \end{pmatrix}$
That is a rotation of angle $\theta$ in the clockwise direction followed by a reflection across the X-axis.