Mat angle question

I think you are asking about 1C (instead of 3, thanks MAT).
Well, you've let cos be c and sin be s, that's a good start. It's a simultaneous equation after all, so... solve it and see what happens?

EDIT: It really depends on how much you know about systems of equations, which renders this problem trivial. Big Spoilers:

Of course, if you don't know this, ignore it for now.

Ok I solved it algebraically and I got 2s+y=c
so 2 sin theta+y= cos theta and so whatever the value of cos theta and sine theta as you,re adding a certain value of y it,ll work for all values of theta. Also where did you get the rotation anticlowise from as you don,t know what direction it,s going.

Ok I solved it algebraically and I got 2s+y=c
so 2 sin theta+y= cos theta and so whatever the value of cos theta and sine theta as you,re adding a certain value of y it,ll work for all values of theta. Also where did you get the rotation anticlowise from as you don,t know what direction it,s going.

If you get the gradients of each line they're -tan(theta) and cot(theta) so theyre perpenicular (product -1) so what can you say about the solution/intersection point existing?

Hmm... hard to parse what you're saying, but that's basically it. When you solve it outright, no value of theta makes x or y undefined.

As for the rotation thing, it's almost kind of a definition. So obviously you wouldn't know if you've never met them before (perfectly normal at this stage). But it would help if you understand what matrices are as transformations (see 3blue1brown's Essence of Linear Algebra).

That it intersects at 1 point

So that pretty much answers the question?

I guess but where do you get the gradient is -tan theta and cos theta

Wait a sec is the rotation anti-clockwise come from the fact that the rotation matrix is costheta -sin theta
Sin theta cos theta
which looks like the thing in the question and you times it by your original point to get an invariant point of (2,1)
Also you get the determinent thing is 1 by doing ad-bc and because the determinant is non-zero it means that it has an inverse so it can work for any value of theta.