sentences:  For example, if the shape is scaled by s and this transformation is denoted by "Ts".then
  "Ts[R(ɸ)] = sR(ɸ)" i.e., all the vectors are scaled by "s".Also, if the object is rotated by "θ" and this transformation is denoted by "Tθ", then
  "Tθ[R(ɸ)] = Rot{R[(ɸ-θ)mod2π],θ}"
  i.e., all the indices are incremented by – "θ" modulo 2π, the appropriate vectors "r" are found, and then they are rotated by "θ".