Can somebody help me
1 answer:
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By Stokes' theorem,
where
is the circular boundary of the hemisphere 
in the 
-
plane. We can parameterize the boundary via the "standard" choice of polar coordinates, setting
where
. Then the line integral is
We can check this result by evaluating the equivalent surface integral. We have
and we can parameterize by
so that
where
and 
. Then,
as expected.
where
where
We can check this result by evaluating the equivalent surface integral. We have
and we can parameterize
so that
where
as expected.
Answer:
Here's what I get.
Step-by-step explanation:
The formula for rotation of a point (x,y) by an angle θ about the origin is
x' = xcosθ - ysinθ
y' = ycosθ + xsinθ
If θ = 270°, sinθ = -1 and cosθ = 0, and the formula becomes
x' = y
y' = -x
A: (-3,4) ⟶ (4,3)
B: (-1,2) ⟶ (2,1)
C: (-2,0) ⟶ (0,2)
The vertices of A'B'C' are (4,3), (2, 1), and (0, 2).
The Figure below shows the triangle before and after the rotation.
