The figure below open cylindrical can, S, standing on the xy-plane. (S has a bottom and sides, but The side of S is given by x² + y2 = 9, and its height is 3. (a) Give a parametric equation, F(t) for the rim, C. F(t) = with SIS (For this problem, enter your vector equation with angle-bracket notation: < f(t), g(t), h(t) >.) (b) If S is oriented outward and downward, find / curl (-3yi + 3xj + 5zk). dÃ.

A fire ant, searching for hot sauce in a picnic area, goes through three displacements along level ground: d→1 for 0.41 m southwest (that is, at 45° from directly south and from directly west), d→2 for 0.52 m due east, and d→3 for 0.77 m at 60° north of east. Let the positive x direction be east and the positive y direction be north. What are (a) the x component and (b) the y component of d→1? What are (c) the x component and (d) the y component of d→2? What are (e) the x component and (f) the y component of d→3? What are (g) the x component and (h) the y component, (i) the magnitude, and (j) the direction of the ant's net displacement? If the ant is to return directly to the starting point, (k) how far and (l) in what direction should it move? Give all angles as positive (counterclockwise) angles relative to the +x-axis.

i have a vector equation r(t)= If and the parametric equations are そミ-7+ Does this describe the same line?

Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.