I'm struggling to understand the intuition behind this because I am unsure which coordinates I am mapping to. I think that I understand how to find the kernel (by essentially finding the null space of the matrix after multiplying the rotational matrix with that of the projection), but I think that I recall having to map coordinates from a preimage to form the image under T (this could be wrong)? And when it says that T is a rotation followed by a projection, I am not sure if this means that we were initially looking at a graph under a rotation, or if we were initially looking at some graph 'X' that was transformed by a rotation and a projection.
If someone could clarify how I should be thinking about a problem like this, I'd be very grateful. My apologies if I am completely off the mark / sound like I'm blabbering on about nothing. I think that this is partially augmented by the fact that I'm having trouble understanding the formal purpose of a kernel and an image.