Compute the Jacobian of the Transformation T Given By $x = \sqrt { 2 } u - \frac { 1 } { \sqrt { 2 } } v$

question 97

Essay

Compute the Jacobian of the transformation T given by $x = \sqrt { 2 } u - \frac { 1 } { \sqrt { 2 } } v$ , $y = \frac { 1 } { \sqrt { 2 } } u + \sqrt { 2 } v$ . Compute the area of the image of $S = \{ ( u , v ) \mid 0 \leq u \leq 1,0 \leq v \leq 1 \}$ and compare it to the area of S.

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Definitions:

Fixed Selling Expense

refers to selling costs that do not vary with the volume of sales, including salaries of sales personnel and advertising expenses.

Variable Selling Expense

Variable selling expense refers to costs that fluctuate with the volume of sales, such as commissions and shipping charges.

Traditional Format Income Statement

A financial statement format that separates operating activities from non-operating activities to reveal gross profit, operating income, and net income.

Contribution Format Income Statement

An income statement format that separates variable and fixed costs, making it easier to see the contribution margin.