Each rectangle has 4 corners and 4 sides. If either corner are within the boundaries of the 4 sides of the other rectangle, or if a diagonal of one rectangle cross a diagonal of the other, they collide.
First, calculate the positions of all the corners, if you know your geometry this shouldn't be too hard.
From here on, vector maths will make it all a lot simpler, go read on the topic if needed. For this purpose we need only points, vectors and the concept of dot products, you can leave the more advanced stuff for later.
Specifically the property that the dot product of two vectors is positive if the angle between them is acute, and negative if it is obtuse is needed.
Look at my beautiful drawing, the angle between vector
b is acute, this tells us that the point
b is pointing to is on the inner side of
d has the opposite property, so
d is pointing to a point outside the rectangle. Perform such a check for each of the 4 sides.
For the crossing diagonal part, you can check if two line pieces intersect by constructing a quadrilateral first taking an endpoint from the first line, then one from the second line, then the other endpoint from the first line, and finally the other endpoint of the second line. If the figure is convex, the lines pieces intersect. To find if a polygon is convex, you can take the determinant of each side as a vector and the following side, if either all of the results are positive, or all negative the polygon is convex.
One of my previous answers might prove useful: Vector problem: which one is the left / centre / right one?