8) Rectangle GHJK with vertices G(2,3), H(2, 5), J(6, 5) and K(6, 3) is rotated 180° about the origin to make rectangle G'H'J’K'. F (x, y)→(-x, y) G (x, y) > (-х, -у) Н (х, у) —> (-у, х) J (x, у) —> (у, -х)

13. [P] Particle 1 starts at point (3, 1, 1) and particle 2 starts at point (10,5,-4); at t = 0, both particles begin to move along linear paths. After 1 second, particle 1 is at point (4, 3, 4) and particle 2 is at (8, 6, 3). (a) Do the paths of the particles intersect? (b) Will the particles collide?

6. (10) Is the transformation defined by T(x,х2) Explain. 3D (2х,, Зх, -5х2, —х, + 1) linear?

Calculate Sc (6(x² − y)i + 5(y² + x)}) · dř if: (a) C' is the circle (x − 8)² + (y − 7)² counterclockwise. Sc (6(x² − y)i + 5(y² + x)}) · dř = (b) C' is the circle (x − a)² + (y − b)² = R² in the xy -plane oriented counterclockwise. Sc (6(x² − y)i + 5(y² + x) x)j). dř = 16 oriented =