PLS EXPLAIN ME ROTATION OF MATRIX THROUGH ANGLE 0(theta) ...also give an example ..!!!

Dear Student,
Please find below the solution to the asked query:

To rotate a column matrix also called a column vector, through an angle θ, we multyply it by the rotation matrix Rθ.In two dimensions, the rotation matrix for angle θ has the following form:Rθ=cosθ-sinθsinθcosθSuppose we have a vector v=2i^+3j^Or, v=vxvy=23If we want to rotate this vector by, say, 30°, we multiply the vector by R30°.That is, the rotated vector,v'=Rθ×vOr,vx'vy'=cosθ-sinθsinθcosθ×vxvyvx'vy'=cos30°-sin30°sin30°cos30°×23vx'vy'=32-121232×23vx'vy'=32×2+-12×312×2+32×3vx'vy'=3-321+332vx'vy'0.232053.5981The rotated vector is,v'=0.23205i^+3.5981j^Refer the figure. The vectors before and after rotation are shown in it.

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