Primary productivity is most influenced by (select all that apply.)

Very small organisms with low Reynolds numbers are most affected by

Which of the following are challenges of life in the rocky intertidal zone? (Select all that apply.)

Which of the following are possible effects of a harmful algal bloom (HAB)? (select all that apply.)

The abbreviation PET stands for __________.

Find the point of intersection of the plane x + 2 y + 3 z = 8 x + 2y + 3z = 8 with the line ⟨ 6 , 1 , – 5 ⟩ + t ⟨ 1 , 0 , – 2 ⟩ \langle 6, 1, -5 \rangle + t \langle 1, 0, -2 \rangle .

Determine the tangent line to the curve r ( t ) = ⟨ t , t 2 + 3 t , t 3 ⟩ \mathbf{r}(t) = \langle t, t^{2} + 3t, t^{3} \rangle at the point where t = 1 t = 1 .

Use Lagrange multipliers to determine the maximum value of  f ( x , y ) = 2 x – 3 y f(x, y) = 2x – 3y subject to the constraint x 2 + 3 y 2 = 12 x^2 + 3y^2 = 12 .

Consider the set of points ( x , y , z ) (x, y, z) given by y ≤ 0 y \le 0 , x 2 + y 2 ≤ 4 \quad x^{2} + y^{2} \le 4 , and 1 ≤ z ≤ 4 \quad 1 \le z \le 4 . Which of the following describe this set of points in cylindrical coordinates?

Use the Divergence theorem to compute the integral of the vector field F ( x , y , z ) = ⟨ x 3 + y 3 , y 3 + z 3 , z 3 + x 3 ⟩ F(x,y,z)=\langle x^3+y^3,y^3+z^3,z^3+x^3\rangle over the sphere of radius 1 centered at the origin.