Determine the image of the point (-5, 2) under a rotation of 90° about the origin.
(-2,-5)
12,5)
(2,-5)
(2,5)

  (2, 5)

Step-by-step explanation:

Rotation clockwise 90° can be accomplished by the transformation ...

  (x, y) ⇒ (y, -x)

so

  (-5, 2) ⇒ (2, 5)

intensity of the vector is v= √37 ≈ 6.08 units and make angle ∡α ≈ 9.46° with east direction

step-by-step explanation:

required vector is consists of the two componentsvx= 2+4=6 units   and vy= 1 unit and vx ⊥ vywe will use pythagorian theorem to find intensity of the vector vv∧2 = vx∧2 + vy∧2 => v = √vx∧2 + vy∧2 = √6∧2 + 1∧2 = √36+1 = √37 ≈ 6.08 unitsthe angle ∡α between vector and east direction we wil find with tanαtanα = 1/6 => α = arc tanα = arc 1/6 => α ≈ 9.46°

hope this