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Question 1 {15 marks) Figure Q1 shows a coordinate frame {A}. Here 1"; is pointing out of page according to the right- hand rule. The frame {A} is rotated by 3' = 20" about l; into a new coordinate frame {3}. (a) (b) (C) (d) (9-) U) {A} .. A ZA Figure 01: Illustration of frame {A}. Plot a gure to schematically illustrate the coordinate frame {B} based on the illustration given in Figure Q1. List formula to calculate the rotation matrix ER and present number result. Demonstrate that the $1? is orthonormal by calculation. A position vector is expressed in {A} as AP = [1 0 2]T. Calculate its position in {B}, i.e., RF. A position vector is expressed in {B} as 3P = [1 D 2]T. Calculate its position in {A}, i.e., AP. Calculate determinant of ll, i.e., IRI