You should be able to do this in your head. Hint: This is a rotation matrix. [cos(0) sin(0) [sin(0) cos(0) - 0] -1 cos (0) x -sin (0) sin (0) x cos (0) x

Q: a h is transformed to the diagonal form D=T'AT, where h b The matrix A = cos 0 sin e T = - sin e…

A:

Q: 9. Find dy: 3 34 (a) 3x³y² + 6xy - y³ — 2x²-5x-1=0 3 (b) x²³cas (1+²) = 2√² - x + 1

A: Given,(a)

Q: b) f(x) = sin(2(x + 60°)) + 3 f (x) = sin x f(x) = sin(2(x + 60°)) + 3 %3D 3.8 90° 90 180° 180 270°…

A: f(x)= sin(2(x+60°) +3 For finding value of f(x) at x= a find f(a)

Q: Consider the function. f(x, y) = 6 – -% 5 4 Find Duf(7, 6), where u = cos(0)i + sin(0)j. (a) 0 = 4…

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Q: Solve using Fourier analysis U=U + 4 cos(2x), u(0,t) = 0, u(r, t) = 0, u(x, 0) = sin(3x) + cos(2x).…

A: Using separation of variables and Fourier series expansion.

Q: a. Prove that the O.D.E: (2y+2x-5)dx+(6y+2x-1)dy=0 is exact and solve it.

A: First we will check if this equation is exact.

Q: Question: 1. Determine the Fourier transform of the signal: f(t) = e4+J5t .cos(2t)

A: The given signal: To find the Fourier transform of the signal: The formula of Fourier transform:…

Q: Describe the transformations that would transform AABC into AA'B'C' and give the transformation…

A: The ∆ABC is given in figure. It is transformed as ∆A'B'C'. Describe the transformation and provide…

Q: 12. In Section 3.2, we saw the rotation matrices: cos(0) -sin(0) [rote] sin(0) cos(0) Express each…

A: (a)

Q: – 10x J (2x – 3)(x + 5) 11 - - Evaluate + C

A:

Q: π/2 sin3 (4 ) αθ - π/2

A: To evaluate the following integrals

Q: Consider the 2n-periodic function f(x) = cos²(x) + sin³ (x). (i) Calculate the Fourier coefficient…

A: Here given that for 2π periodic function, f(x)=cos2(x)+sin3(x). We calculate a0,a1,a2,an(for…

Q: Compute the Jacobian A. I = 5u OB. I = 5u (cos² (5v) - sin² (5v)) O C. I = 0 (x, y) d(u, v) ○ D. I =…

A: A detailed solution is given below.

Q: Problem #2: Consider the function f(x) = 7+ 8 sin²(6x) restricted to the interval [-7, 7]. Calculate…

A:

Q: P(₁,0) = (rcos, y sin e). What is the image under P of the rectangle [0₁1] x [0₁] P ([0, 1] x [0,TT]…

A: Given that .We need to find the image under  of the rectangle .We know that, for a positive real…

Q: Is w = cos(z) a fractional linear transformation

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Q: f(x) = Jsinx 02x>N T >x22n

A:

Q: given the following transformation [1 cos (0) -sin (0) 2 Iab = sin (0) cos (0) 3 1 a) What is the…

A: We will answer the first question since we answer only one question at a time. Please resubmit the…

Q: tation by an angle 0 can be written in matrix form as: [cos(0) - sin(0)] sin(0) cos(0) Use this and…

A: For this we may take two figures as follows:

Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

A:

Q: Could you please find this model B's inverse with the adjoint method

A: Firstly evaluate the determinant of the matrix B. B =1-10-b10-g01 =1[(1)(1)-(-1)(-b)]…

Q: QUESTION 9 (s+3)² +9 e*[cos(3t) – sin(3t)] O e-3[cos(3t)- sin(3t)] e-3[cos(3t) – 3sin(30)] O e…

A: The given function is  [S/{( s+3)^2 + 9}]  In this problem we use the shifting properties of Inverse…

Q: Question t s). Show that a reflection about the line y = x is equivalent to a reflection in y…

A: Given a point P is reflected cross the line y=x the new point after the transformation is P'.…

Q: 6.) Find the Jacobian of the transformation = u cos 8 - v sin 6, y = u sin 6 + v cos 6

A: Given Data: x=ucosθ-vsinθ ......1y=usinθ+vcosθ ......2   The partial derivative of equation (1) with…

Q: Mesh – current analysis produces the following two equations: (5 – j4) I – (-j4)l, = 10040° (4 + j3…

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Q: QUESTION 8 Determina la razón de cambio promedio (ARC) de la función f (x) =x +x4 entre x 0 y x 2

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Q: AB14

A: