0 e₁ = -(6), ₁-(i). P=(-2₂). = Р -(33). 0 Let a) Find an orientation-preserving isometry for m: R2 R² so that m(e₁)=p, m

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0 e₁ = -(6), ₁-(i). P=(-2₂). = Р -(33). 0 Let a) Find an orientation-preserving isometry for m: R2 R² so that m(e₁)=p, m (e₂) = q Express m in the form m (x) = 4x + v where A is an orthogonal 2×2 matrix and v E R². Explain why m is a rotation and determine the angle and centre of rotation. Hint: Consider m (e₁) - m (e₂) b) Find an orientation-reversing isometry for m': R² R² so that m'(e₁) = p , m' (е₂) = q Express m in the form m'(x) = A'x+v where A' is an orthogonal 2×2 matrix and v E R². Explain why m' is a glide reflection and determine mirror line and translation vector. c) Explain why m and m' are unambiguously determined. q=