Suppose a change of coordinates t: r2→r2 from the uv-plane to the xy-plane is given by x=4v−2u−3, y=−1+5u+4v.

(a) find the absolute value of the determinant of the jacobian for this change of coordinates. ∣∣∂(x, y)/∂(u, v)∣∣= ∣det |=

(b) if a region d∗ in the uv-plane has area 7.04, find the area of the region t(d∗) in the xy-plane. area =

step-by-step explanation:

a rhombus is a parallelogram enjoying his symmetry.

1/4 because there is 4 grades.

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west

      2

  2 is to go somewhat to the top right of a because it is squared    

v= a h/3