/sci/ - Science & Math

Doing homework and there's only one task left that I am stuck on

Say you have an ordinary coordinate system K with coordinates x and y, with the normed basis vectors ex and ey
A vector R that we assume is in the first quadrant can be written as x*ex+y*ey
A new coordinate system is introduced, called K'. This has coordinates x' and y'. Origin in this system located at the origin of K so we can say that it's almost like K just rotated θ degrees in positive direction relative to K

R can be decomposed in K' as
[math]x'\vec{e}_{x'}+y'\vec{e}_{y'}[/math]
The basis vectors in the coordinate directions x' and y' are normed
>>Find the coordinate position (x', y') relative to K' by the coordinate position (x, y) relative to K


At first I thought I would just do a coordinate changing using an inverse matrix of K but of course, that won't work in this case