a. I've attached a plot of the surface. Each face is parameterized by
•
with
and
;
•
with
and
;
•
with
and
;
•
with
and
; and
•
with
and
.
b. Assuming you want outward flux, first compute the outward-facing normal vectors for each face.





Then integrate the dot product of <em>f</em> with each normal vector over the corresponding face.










c. You can get the total flux by summing all the fluxes found in part b; you end up with 42π - 56/3.
Alternatively, since <em>S</em> is closed, we can find the total flux by applying the divergence theorem.

where <em>R</em> is the interior of <em>S</em>. We have

The integral is easily computed in cylindrical coordinates:


as expected.
Answer:
magnitude: 21.6; direction: 33.7 degrees
Explanation:
When we multiply a vector by a scalar, we have to multiply each component of the vector by the scalar number. In this case, we have
vector: (-3,-2)
Scalar: -6
so the vector multiplied by the scalar will have components

The magnitude is given by Pythagorean's theorem:

and the direction is given by the arctan of the ratio between the y-component and the x-component:

It is not possible to see the other waves on the electromagnetic spectrum because only other species can see the other parts of the spectrum because they have different components in their eyes than we do, therefore, only allowing us to see a
portion of the spectrum, which is visible light.
Elements with the largest atomic radius are found in the lower left hand of the periodic table.