What is the Formula Derivation to find new coordinates when axes are rotated?

What was the old coordinates of point A(2,5) if coordinate axes is rotated by 30^(@) in clockwise direction.

Line L has intercepts a and b on the coordinate axes. When, the axes area rotated through a given angle, keeping the origin fixed, the same line L has intercepts p and q , then

The line L has intercepts a and b on the coordinate axes. The coordinate axes are rotated through a fixed angle, keeping the origin fixed. If p and q are the intercepts of the line L on the new axes, then (1)/(a^(2))-(1)/(p^(2))+(1)/(b^(2))-(1)/(q^(2)) is equal to

Thu Line L has intercept a and b on the co- ordinate axes.When keeping the origin fixed, the coordinate axis are rotated around a fixed angle,then the line has intercepts p and q on rotate axis,then

The transformed equation of x^(2)+3y^(2)+2xy=2 when the coordinates axes are rotated through an angle of (67 1/2)^@ is AX^(2)+BY^(2)=1 then A+B=

How the equation is transformed when origin is changed and axes is rotated?