The curves C₁ and C₂ have polar equations C₁: r = 1/√2, for 0 < θ < 2π, C₂: r = √(sin10), for 0 ≤ θ≤ π. Find the polar coordinates of the point of intersection of C₁ and C₂. Sketch C₁ and C₂ on the same diagram. Find the exact value of the area of the region enclosed by C1, C2 and the half-line θ = 0.

OR The linear transformation T : R⁴ → R4 is represented by the matrix M = (-1 2 3 4; 1 0 1 -1; 1 -2 -3 a; 1 2 5 2)

The curve C has polar equation `r = a sec²θ`, where a is a positive constant and `0 ≤ θ ≤ 1/4π`.

The curve C has polar equation r = e^(-θ) - e^(-1/2π), where 0 ≤ θ ≤ 1/2π.

The linear transformation T : R⁴ → R⁴ is represented by the matrix M, where M = [[1, -3, -1, 2], [4, -10, 0, 2], [1, …

The square matrix A has λ as an eigenvalue with e as a corresponding eigenvector. Show that e is an eigenvector of A²…

The plane Π₁ has equation r = [[2], [3], [-2]] + s[[1], [0], [-1]] + t[[0], [-1], [-2]]. Find a cartesian equation of…