Question 1
Find

dV
2(
x), where M is the 2-manifold in R
4 given parametrically by

for 0 ≤ u ≤ 1, 0 ≤ v ≤ 1.
Question 2
True or False: The k-volume of a k-parallelogram in R
k spanned by the k vectors v
1, v
2 ,......, v
k is given by det(A), where A is the k × k matrix whose columns are the components of the vectors

.
◦ true
◦ false