Hello, I am stuck on a question in my FP1 textbook, in the practice exam section. I'm doing the OCR board.

It tells me that there are two 2 x 2 matricesRandSrepresent the following transformations in the x-y place.

R: a rotation through angle θ anticlockwise about origin

S: a stretch with scale factor 2 parallel to the x-axis (with the y-axis invariant)

RSR-¹is denoted byM

I have found thatMis:

$\displaystyle \left(

\begin{array}{cc}

1 + cos^2 \theta & sin \theta cos \theta \\

sin \theta cos \theta & 1 + sin^2 \theta

\end{array}

\right)$

The next part says the the pointPhas the column matrix:

$\displaystyle \left(

\begin{array}{c}

x \\

y

\end{array}

\right)$

And that the pointQis the image of P under the transformation represented byM.

I have found that the column matrix of Q would be:

$\displaystyle

\left(

\begin{array}{c}

x + xcos^2 \theta + ysin \theta cos \theta \\

ysin \theta cos \theta + y+xsin^2 \theta

\end{array}

\right)$

But the next part asks me to show that the line joiningPtoQmakes an angle θ with the x-axis.

How would I show this last part? O____O Please help me and thank you very much in advance.