given the following transformation [1 cos (0) -sin (0) 2 Iab = sin (0) cos (0) 3 1 a) What is the rotation axis? 01
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Q: is transformed to the diagonal form D= 1"'AT, where h b The matrix A= %3D cos 0 sin0 T= -sin 0 cos0…
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Q: (A) Find Laplace transform of the function : f(t)=1 sin(2t+) cos(21-7)
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Q: Question 3: Evaluate the Fourier transform of a Gaussian g(x) = ae with a, b>0 %3D
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Q: 1) On the table of Laplace Transforms, you might see the formula L = ett sin(bt) (s-a)²+b? . Without…
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Q: 6.) Find the Jacobian of the transformation = u cos 8 - v sin 6, y = u sin 6 + v cos 6
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Q: - Find the Laplace transformation of the following: 1) (2t² – 1)2 2) cos³t 3) sinh³t Hint: sinh?t =…
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Q: 1: Find the trigonometric Fourier of the triangular waveform shown over the interval (-TT, TT). x(t)…
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Q: Question # 1: Find the Fourier transform of the following Signals x(t), and y(t). X(1) (-) + 2 er ()…
A: The formula for the signals xt is, xt=ut+2+ut+1-ut-1-ut-2 Let, xt↔FTXjw Then, xt+T↔etJwTXjw
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Q: Find the Laplace transformation of the following: 1) (2t2 – 1)2 2) cos³t 3) sinh³t Hint: sinh?t =…
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Q: 1. Use the tables to find the z transforms of the following j. 2n k. (-3) 1. sin(nπ/2)
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Q: Determine the following Laplace transforms: i) L cosh at) i) -35+9 iii) Ls +5 7-23+1 2s+1 iv) Ls+…
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Q: Question 1.i.) A truncated sine wave sin5x, -T < x < T y = f(x) = 0, otherwise Find the Fourier…
A: Since you have asked multiple question, we will solve the first question for you. If youwant any…
Q: b. Find the eigenvalues for the rotation transformation in R? |cos e - sin 0 sin 0 Cos O
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Q: QUESTION 14 The Laptace transform of )-te'sin(2r) is 4(s+ 1) 4(s-1) (s-1)+4) 2. -1)+4 B. 2(s- 1)…
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Q: Find the z-transform of the following equations: b. cos(3n) + 2 sin(3n)
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Q: 9.45.) (a) Use the figure to show that x =r cos ø, y = r sin ø and x' = r cos( ø – 0),y' = r sin (4…
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Q: Find the Jacobian of the transformation. x = 5a sin ß, y² 4α cos β
A: By finding first derivatives and determinant as the formula of jacobian you can solve the given…
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- In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is weird, in that it takes precisely 2π hours for the hour hand to do a full rotation. Let’s position the clock in the xy-plane so that the center of the clock is at (0, 0), and the tip of the hour hand at "midnight" is at (0, 1). (a) It follows from the definition of sin and cos that at time t, the tip of the hour hand is at position (x, y) = (cos(t),sin(t)). Check that this makes sense by “manually” finding the position of the clock at time t = 0, π/2 , π, 3π/2 , and 2π. (b) The equation describing the circle that the hour hand traces out is x2 +y2 = 1. We’re going to calculate how fast the x-coordinate of the tip of the hour hand changes with time. We’ll do this in two ways. Using the fact that x = cos(t), what is dx/dt ? (c) Next, we’ll compute dx/dt in another way. Using the fact that y = sin(t), what is dy/dt ?In math land, there is a clock. The hour hand of this clock is 1 ft long. However, the clock is weird, in that it takes precisely 2π hours for the hour hand to do a full rotation. Let’s position the clock in the xy-plane so that the center of the clock is at (0, 0), and the tip of the hour hand at "midnight" is at (0, 1). (a) It follows from the definition of sin and cos that at time t, the tip of the hour hand is at position (x, y) = (cos(t),sin(t)). Check that this makes sense by “manually” finding the position of the clock at time t = 0, π/2 , π, 3π/2 , and 2π. (b) The equation describing the circle that the hour hand traces out is x2 +y2 = 1. We’re going to calculate how fast the x-coordinate of the tip of the hour hand changes with time. We’ll do this in two ways. Using the fact that x = cos(t), what is dx/dt ? (c) Next, we’ll compute dx/dt in another way. Using the fact that y = sin(t), what is dy/dt ? (d) Next, use implicit differentiation to find dx/dy . Express your answer…Prove that a rotation of θ = π/4 will eliminate the xy-term from the equationax2 + bxy + ay2 + dx + ey + f = 0.
- Graph the line and conic section. r = 8/(4 + cos u)Determine the equation of the given conic in XY-coordinates when the coordinate axes are rotated through the indicated angle. x2 − y2 = −4y, ϕ = cos−1 3/5If P1 and P2 are two points on the conic whose angles θ1 and θ2 differ by 180° , show that the harmonic mean of their respectivve values of r is a constant ( you will need to look up what harmonic mean is).
- Given 7x^2 - 6sqrt(3)xy - 13y^2 - 16 = 0 A new equation after rotation using x = x'cos(theta) - y'sin(theta) and y = x'sin(theta) + y'cos(theta) becomes (x')^2/4 - (y')^2 = 1 Find the vertices of the conic in the xy-planeA lizard moves through the plane with its position at t seconds given by the parametric equations x=3cos(2pi t)+2, y= -6cos(2pi t)+1. The lizard begins moving at t=0 seconds. a. How long does it take for the lizard to return to its starting position for the first time? b. how far does it go in 4 seconds?Find the image equation of the line −2x + y + 3 = 0 under the rotation about C = (1, 1) at an angle ? = 90°.
- Consider a particle traveling clockwise on the elliptical path x2/ 100 + y2/25 = 1. The particle leaves the orbit at the point (−8, 3) and travels in a straight line tangent to the ellipse. At what point will the particle cross the y-axis?3. (c) I not only want the diagram but also the procedure to make a bifurcation diagram4. Find the exact length of the polar curve r = e2θ, 0 ≤ θ ≤ 2π.