Write down the 3 x 3 matrix that rotates a 2D point by angle about a point 0 p = (xp, yp).

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Q: 4. Let the function x(1) be given by the conditions x (0) = 1 and x(1) = 1x(1) + 2[x(1)]² S…

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Q: Az = b, where A = (A) 7/6 1/6 (D) [2/3] 1 3 b = 189 11 [Q] X2 Compute projcol(A) (b), the projection…

A: The matrix .The objective is to find the projection of  onto .

Q: 8) Prove that 2 is a primitive root modulo 53.

A: We have to Prove that 2 is a primitive root modulo 53.

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A: (1)  Given that…

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Q: ·0-0-0 6= Az = 6, where A = How many least-squares solutions does this system have? (A) 0 (D)…

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Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

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Q: What is an example of a graph that has a Hamiltonian cycle but contains no Euler cycle.

A: What is an example of a graph that has a Hamiltonian cycle but contains no Euler cycle.

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Q: prove that 11 ㅣㅣㅣㅣ 리 ZtZ3 < 1211 12월 18

A: For complex numbers z2,z3 with

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Q: (10) Find all solutions of the congruence 2 = 22 (mod 53). C

A: We shall be using primitive roots to solve this congruence.

Q: Use the power reducing formulas to rewrite cot23x sin 3x in terms of the first power of cosine.…

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Q: Use the adjoint method to find the inverse: 4 3 2014 5 -37 15 1 -19 15

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Q: Find the corresponding linear system near each critical point.

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Q: Two dice are rolled. Find the odds in favor of rolling the following. ​(a) A sum of 5 ​(b) A sum of…

A: The objective of this question is to calculate the odds in favor of rolling a certain sum when two…

Q: whether (-77) n! is convergent

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Q: Question: The polynomials p(x) = x(x - 1) and q(x) = (x - 1)(x - 2) are orthogonal when the inner…

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Q: 7. Let fn [a, b] R be Riemann integrable and suppose that fn →f uniformly on [a, b]. (a) Prove that…

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Q: The surface integral is rewritten incorrectly. F((x, y)) is incorrect. The tangent vectors T, and T,…

A: We will identify the first error in the given work shown.

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Q: Calculate the proximity to each other and the angles of each location using Law of Cosines to each…

A: To calculate the proximity (distance) between two locations and the angles formed by these locations…

Q: 1. A lifeguard standing at the water’s edge sees a man flailing out in the water. She runs along the…

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Q: Let f(x) = x x+1 g'(x) = X . Calculate g'(x), where g(x) is the inverse of f(x).

A: Let f(x) = x/(x + 1)We have to calculate g'(x) , where g(x) is the inverse of f(x).

Q: 3 + The graph above can be written as y= = Where f(t) = = a = g(t): = b = || 6 7 8 9 10 = VOLO…

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Q: Find an orthogonal set with the same span (and same number of elements) as 7 -5 4 (D90- -10 7 4 3…

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Q: Solve the following quadratic equations (hint use the quadratic formula) 6x² + x = 12 Find the…

A: The first part of the question asks to solve the quadratic equation 6x² + x - 12 = 0. The quadratic…

Q: D. Find (with proof) the infimums of the sets S = {1/n: n = N+) and T = {(-1)" /n:n € N†}. Is either…

A: and To find: Infimum of the given sets.

Q: 1. In your own words, describe what the vectors in a vector field tell us about the function. Each…

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Q: 24. If the second derivative f" exists at a value xo, show that f(xo + h) - 2f(xo) + f(xo − h) h²…

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Q: 5) Consider the facility location problem that we covered in lecture: 5a) min z = X n m n ΣΣ cijxij…

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS FOR BETTER UNDERSTANDING. x f(x) 0 0…

A: Given table isWe have to find the value of the function at x=482We know thatThe formula for linear…

Q: use the method of variation of parameters to find the general solution to the system.  v'(t)=-g -…

A: Differentiating the given equation we get      v"(t) = 0 - 5v'(t) -120(h'(t)/m)              =…

Q: 1. For each of the following sets of vectors in R³, determine whether the vectors span R³. For those…

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Q: SOLVE THE FOLLOWING PROBLEM AND SHOW YOUR COMPLETE SOLUTIONS FOR BETTER UNDERSTANDING. X f(x) 0 100…

A: From the given tabulated values, the x values are not equally spaced. Hence use Newtons dividend…

Q: 10. Consider the following two 3 x 3 matrices -1 3 3 1 -2 -1 1 -2 -2 (b) A = (c) AB and BA. " and…

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Q: Let f: A->B and X⊆A, Y⊆B define a) image of X and b) inverse image of Y

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Q: ( ) The IVP d²x dt² dx + cos(t). + sin(t)x: tan(t) dt x (1.25) = 12 dx dt 1.25 has a unique solution…

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Q: 5. Find an orthonormal basis for the subspace of R³ given by {(x, y, z)T : x − y+ z =0}

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