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Rotation of a figure about a point p in R2 is accomplished by first translating the figure by -p, rotating about the origin, and then translating back by p. See Fig. 7. Construct the 3 X 3 matrix that rotates points -30° about the point (-2, 6), using homogeneous coordinates.
Fig. 7
The problem you must solve is: How many times louder is a 60 dB sound than a 20 dB sound? How many times more energy is released by a magnitude 6 earthquake than by a magnitude 2 earthquake?
U.C.L.A. states that at least 40% of the students live on campus. From a sample of 250 students, 90 live on campus. Does this sample provide evidence that fewer than 40% live on campus? Conduct the test with a=0.01.
Similarly, one additional unit will be occupied for each 5 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Transform the equation to standard form and find the center and radius of the circle:
The linear equation x=-1 graphs as a horizontal/vertical/diagonal line(choose the correct label). Describe how you determined your answer.
Assume the distribution of food expenditures for the family of four follows the normal distribution, with a mean of $490 and standard deviation of $90.
Prestige Builders has a development of new homes. There are four different floor plans, seven exterior colors, and an option of either a two-car or a three-car garage. How many choices are there for one home?
Estimate the relative error in the calculated surface area.
Let G be a simple graph with no isolated vertex and no induced subgraph with exactly two edges. Prove that G is a complete graph. (Please read carefully the definition of an induced subgraph before you attempt to solve it!).
Find the radius of convergence and interval of convergence for n=1Σ∞xn/√n. Find the radius of convergence and interval of convergence for n=1Σ∞(x - 2)n / (n2 + 1).
Use Euler's method with step size 0.1 to estimate y(1.4), where y(x) is the solution of the initial-value problem below. Give your answer correct to 4 decimal places.
What do you understand from Curl and Div of a vector field F? Explain them with examples. Is there any difference between Grad and Div of F? What are the applications of Grad, Div and Curl? Define Contra positive, Converse, and Inverse of a statement..
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