I looked it up here, a rotation matrix to rotate a vector by an angle θ is [[cos(θ), -sin(θ)], [sin(θ), cos(θ)]].

I did remember that it was something with cosinus and sinus, but: why? How does multiplying a vector with this particular matrix make it rotate? How do I get an intuition for this?

@vaporeon_ if you're truly curious I could share a picture from my undergraduate e&m textbook which goes over this in the first chapter

Also how familiar are you with sin and cos?

@wallhackio Yes, please, do share the picture

Regarding sin and cos: I am aware that they represent the ratio of some sides of a triangle where one of the angle is 90°, and that it's also a function, and that you can define it as an infinite sum (I forgot the terms of the sum, though...), but I lack an intuition for using it to rotate things

@vaporeon_ what are the lengths of x and y in terms of Φ?

@wallhackio I might be misremembering, but I think sin(phi) = y/z and cos(phi)=x/z in this picture, so the lengths would be x=cos(phi)*z and y=sin(phi)*z... Am I wrong?