How to find a co ordinates?

Question

I find the coordinates of given point is at (-8,-5) frm origin under normal coordination system. Now the coordination frame is tilted to 30 degree clk wise and new orgin located at (3,3) in first quadrand of old one.The point remain unchanged in it position. Then what will be the cordinates for that point based on tilted coordination frame.

Answer 1

new cord. = (-5.526,-12.428)
plz let me know whether ans is correct

Answer 2

x(new) = [xcos(30)-ysin(30)] - 3
y(new) = [xsin(30)+ycos(30)] - 3

Note that it's -3 at the end because if the origin is transformed to (+3,+3), all points' coordinates change by (-3,-3)

x(new) = (-8)(1/2) - (-5) (√3/2) - 3
y(new) = (-3)(√3/2) + (-5) (1/2) -3

x(new) = -7 +2.5√3
y(new) = -1.5√3 - 5.5

So your point now lies at (-2.67, -8.10)

Answer 3

rotation matrix:

cos30 sin30
-sin30 cos30

or

sqrt(3)/2 1/2
-1/2 sqrt(3)/2

The given point matrix
-8
-5

Multiply these two matrices:
-4sqrt(3)-5/2
4-5sqrt(3)/2

Answer:
xnew=3-4sqrt(3)-5/2
ynew=3+4-5sqrt(3)/2