The points of the shape after the shear are $(-0.25, 1)$, $(1.75, 1)$, $(0.25, -1)$, $(-1.75, -1)$. Other than that the only other information given is that the vertical edges of the original shaded square have become horizontal (parallel to the x-axis).
I've calculated that the Shear Matrix is:
|x + 0.75y|
| y |
But I don't understand how we're supposed to know what the Rotation Matrix is with the given data.
Any thoughts much appreciated.
The slope of the formerly vertical edges after the shear is clearly $\frac{1}{0.75},$ that is, $\frac 43.$ These sides therefore are at an angle $\tan^{-1}\left(\frac43\right)$ counterclockwise from the direction of the $x$-axis.
You therefore need to rotate those sides (and therefore you need to rotate the whole figure) by an angle that reduces the angle they make to the $x$-axis from $\tan^{-1}\left(\frac43\right)$ to zero.
So you need the rotation matrix for a clockwise rotation by $\tan^{-1}\left(\frac43\right)$ (or equivalent angle), or a counterclockwise rotation by $-\tan^{-1}\left(\frac43\right).$
I suspect the $\frac43$ slope was chosen because it leads to particularly nice values of the sine and cosine that you will need.