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Calculate the standard matrix for each of the following linear transformations T.
a. T: R^2 -> R^2 given by rotating -pi/4 counterclockwise about the origin and then reflecting across the line x_1 - x_2 = 0.
b. T: R^3 -> R^3 given by rotating pi/2 counterclockwise about the x_1-axis (as viewed from the positive side) and then reflecting across the plane x_2 = 0.
c. T: R^3 -> R^3 given by rotating -pi/2 counterclockwise about the x_1-axis (as viewed from the positive side) and then rotating pi/2 about the x_3-axis.
Consider the quadratic expression representing displacement of an object thrown toward earth at an initial velocity of 32 ft / sec from a height of 128 ft.
Solve the given system by the substitution method.4x + y = 217x - 2y = 18
Let G be a finite group which has exactly 8 Sylow 7-subgroups. Show that there exists a normal subgroup N of G such that the index [G:N] is divisible by 56 but not by 49 ??
If the trend continues, determine when the percent of women in the workforce will equal the percent of men. (Provide a graph showing the linear trends and the breakeven point).
Loan amortization, which refers to determining equal annual loan payments, can be implemented by which of the following?
Write the given phrase as a mathematical expression.
Please find a quadratic equation in standard form to model the data in the table. A ball is hit into the air. Its height in feet, s, at time t is given by the equation s(t)=-16^2+25t+4.
use the graph below to write an equation that represents car value depreciation since purchase of the car. use the
What percentage of the people have only cats or only dogs? Find the slope of the line passing through the points (9, 12) and (8, 4).
Solving maximization proplem with graphical method.
A laptop computer is purchased for $1500. Its value each year is about 80% of its value in the preceding year. Its value in dollars after t years is given by the exponential function
With a utility function of U(S,A)= S0.4 x A0.6, derive a set of data points for U=1 and then plot a graph to show this indifference curve. Hint: use maximum values of 9 apples (A) and 27 sandwiches (S).
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