Rotating a Parabola: 30o Anti-Clockwise About Origin

[squenshl]

The parabola y = x² is rotated anti-clockwise about the origin through the angle 30^o. What is the new equation of the new curve (relative to the standard basis)?

 

[Office_Shredder]

If you have a point (x,x²) and you rotate it by 30 degrees around the origin what does it become?

 

[HallsofIvy]

And you can rotate a point (x,y) through an angle \theta about the origin by the matrix multiplication
\begin{bmatrix}cos(\theta) & -sin(\theta) \\ sin(\theta) & cos(\theta)\end{bmatrix}\begin{bmatrix}x \\ y\end{bmatrix}.