a) Translate A ALT if A(-5,-1), L(-3,-2), T(-3,2) by the rule (x,y)→(x+ 3, y+ 2), then reflect the image over the y-axis A'L L'C T'L A"L, L"C 6 -5 4 -3 21 0

Q: FK - R, d(P, P3) = max {|x1 – zal. In – valj, Pa (21.), Pz= (2. 92) 4 the the mapping T(z,y) = (I,…

A: Let (x1, y1), (x2, y2)∈ℝ2 Then T1(x1, y1)=(23x1, 45y1)T2(x2, y2)=(23x2, 45y2) Let…

Q: 4. Let L: R² +R? be the linear map defined by L(x, y) = (x + y, I - y). Show that L is invertible.…

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Q: Suppese That z is guen in implicit form by the equation : X°y -yz?+ X = 16 enviroment %3D in an of…

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Q: Q2:- Evaluate / x + ydA where Ris the trapezoidal region with vertices given by R 5 5 (0,0), (5, 0).…

A: To find - Evaluate ∬Rx + y dA where R is the trapezoidal region with vertices given by…

Q: Ôz and Show 4. Use an appropriate form of the chain rule to find dv (a) z3x²-y tanx, x =u/v, y = u'v

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Q: Let ūi= 3. 5 %3D and u = Uz %3D Is V= 田。 e Span

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Q: 10) a) What is a rigid motion (isometry)? 11) Are the two figures congruent? Explain why or why not…

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Q: for transformation x=au + bv, y=bv+cw, z=cw jacobian value J(u, v, w) = ...

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Q: Determine the location of a point (x, y, z) that satisfies the condition  ∣y∣ ≤ 3

A: If ∣y∣ ≤ 3 the point lies with in 3 units from xz plane on left side if y < 3 , or within 3 units…

Q: B. Sketch these Cartesian products on the x-y plane R² (or R for the last two). 9. {1,2,3} x…

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Q: THEOREM 4.4 (LINEAR TRANSLATION) Let Y= aX + b; then: My(0) = eb" My(a0).

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Q: Find the EXACT Jacobian a(x,y) d(u, v) 1 1 - -— (9u - 4v), y = —— (3u +3v) 4 4 X = for the following…

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Q: [2 Lo 2. and defined T: R² → R³,by T(X) = AX. Let A Find the images under T of u = |E|, and v =

A: Given a linear transformation T:R2→R3 by T(X)=AX where A= 2002

Q: The notation (x, y) (1.5x, 1.5y) defines a rotation in the coordinate plane. O True O False

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Q: The notation (x, y) (y, x) defines a reflection in the coordinate plane. O True O False QuickNa

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Q: 2. Use the transformation u = x – 2y, v = 2x + y to find x – 2y 2.x + y Where R is the rectangular…

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Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

A: Given, Xi~χ12 ,i=1,2,...,n a. Y=∑Xii=1n Therefore, X1+X2+.....+Xn~χn2 above is possible using…

Q: Let A = = اه هب را ره and ve lation R, R2R3 and Ry on A, what Would graph be their directed ام مه…

A: R1=a,a,c,c,b,b,d,d The directed graph is:

Q: The notation (x, y) → (-x, y) defines a reflection on the coordinate plane, O True O False

A: Solving the problem by helping of a point.

Q: The transfomation takes points from the xy plane to v= 3x Jx=? that takes points from the uv plar V=…

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Q: 1. Let F(x, y, z) = (x + y², y + z²,z +x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: by using guass divergence theorem

Q: Let f(x, y) = 2x² + 5xy + 2y² + 5x – 5y + 2. Find the linearization L(x, y) of f(r, y) at the point…

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated change of variables. - 1/2 (u = v), y = 1/2 (u…

A: Jacobian ∂(x,y)/∂(u,v)= ∂x/∂u* ∂y/∂v - ∂y/∂u* ∂x/∂v

Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: 2 -2 0 -2 What are the coordinates of the image Ri90, o)(JKLO) = J'K'L'O? %3D J=(-3,1 K' = (-1,-5…

A: Find the points after rotation

Q: (ii) Use the rescalings s = S/N, i = I/N, t = BN1, c = µ/(BN) and d = y/(BN) to non-dimensionalise…

A: differential equation representing disease with classes S , I , R dSdt=-βSI+γRdIdt=βSI-μIdRdt=μI-γR…

Q: What is the rule used to transform ΔABC to its image?   A(−3, 5), B(2, 8), C(−4, −5) and A'(−3,…

A: Given ,  A(-3 , 5) , B(2 ,8) , C(-4 , -5) and A'(3 , -5) , B(2 , -8) , C(-4 , 5) We have to find…

Q: Transform pentagon BEARS according to (xy) → (x + 6, y+8). Write the coordinates for pentagon…

A: Given Data: Traformation: x, y→x+6, y+8   The given figure in the problem represents the pentagon…

Q: Find the image of (2, –2) after a counterclockwise (passive) rotation of the axes about the origin…

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Q: 2. Show that the equations f(r, y,P. q) = 0 and g(r, Y.P. q) = 0 are compatible if %3D %3D a(f,g)…

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Q: Transform pentagon BEARS according to (x, y) → (x +6,y+B). Write the coordinates for pentagon…

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Q: - 3 - 2 Let y = u2 = Find the distance from y to the plane in R' spanned by u, and u2. - 6 u = - 5 1…

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Q: 1 -1 1 Let W Span U1 %3D and y = 1 3 Then, the distance from y to W is 11

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Q: The notation (x, y) → (-x, y) defines a reflection on the coordinate plane. O True O False

A: In coordinate plane for reflection over x axis for reflection over y axis

Q: ) Let f(r, y) = e5v-8z. Find the linearization L(x, y) of f(x, y) at the point (0, 0). L(x, y) =…

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Q: a +c b+c b) h(a + bx + cx?) = %3D 1+b+c, Is this mapping linear?

A: Given : h(a+bx+cx2)=a+cb+c1+b+c To Find : Determine the given mapping is linear.

Q: 22. Find the Jacobian ô(x, y, z)/a(u, v, w) of the transformation а. х 3D и соs v, у 3D u sin v, b.…

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Q: Draw a direction field for the equation y'=y+x-y^2 for -5 < x, y <5, and include the integral curves…

A: The direction field is obtained as follows:

Q: Let F = (3y + 2) i + (4x – 22) 7 + (3x – y) k Find Sc FdF where C is a line segment 8. %3D from A(2,…

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Q: 2. Let u(x, y) = 2+ 3.x – y + x² – y? – 4.xy. Show that u(x, y) is harmonic and find the harmonic…

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Q: ue or False. Let x, y E R". If || + y = ||x – y||, then x cannot be orthogonal to y.

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Q: Find the linearization L(x,y,z) of the f(x,y,z)= 8 square(x^3+y^3+z^3) at the point (1,2,3)

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Q: c) Use the Chain Rule to compute %3D ds se In (c) express your answer in terms of the independent…

A: Here, the given functions are: f(x,y,z)=x4y+z4, x=st2, y=st,z=s2t

Q: Find the linearization L(x, y, z) of the f (x, y, z) = 2/³ + y³ + z³ at the point (1, 2, 3 Answer:…

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Q: 1. Let T: R3 R3 be a linear image, which satisfies that (-3 Tei = -3/22, T(ez) = 9/2 and T (es) = -3…

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Q: The notation (x, y) (-x, y) defines a reflection on the coordinate plane. O True O False

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Q: Given F(x.y.z) (x+y+Zi +(x-yj+(xz-2)k what is CurlF at the point (1,-1,3)? You should write your…

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Q: 6. Let f(u, v) = u sin(v) – v cos(u) and u(r,y) = r² – ry² v(r, y) = y – r Find af af and both by…

A: We need to find the derivatives using direct substitution and by chain rule . Now , we have ,…

Q: Let ƒ (x, y) = x² - y² . Find all all points (x, y) such that Vf(x,y) =±(1, 1).

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