1 1 1 Q2\ If Z =2+j, z, =-2+ j4 and Z3 =-+ - evaluate z, in the form %3D z, x+jy and in polar form.

Q: [2.18] Derive an explicit form of the polar C* of the following cones: a. C= {(x),x2):0 x2 s2x1}. b.…

A: To find- Derive an explicit form of the polar C* of the following cones: C = x1, x2 : 0 ≤ x2 ≤ 2x1…

Q: Compute using polar coordinates SS. y dA where S is the area of region in first quadrant ewtsi (b)…

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Q: [] -3 -3 Let y = -9 uj -5 u2 5 Find the distance from y to the plane in R3 spanned by ul and u2.

A: Consider the provided question,

Q: QUESTION 8 Let A=Z and R ={(x,y)EA×A; x=y+1 or x=y – 1} Select the properties of R: Antisymmetric…

A: Relation

Q: Find f -6xydA over the triangular region D with vertices (0,0) (2,0), (0, 4) O68 -68 )-8 -16 16

A: Consider the integral

Q: 0 2 1 2 -1 2 -2 Problem 9 · Find the Schur triangularization of (a) A = and (b) A = 1 2 0 1 -1 3

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Q: Q : Let: z, 1-i and z2 = V3+i. Find z, 22 in the polar forn

A: Explained below...

Q: The conjugate z of z=x+iy is z=x-iy

A: 4) Conjugate of a complex number: The complex conjugate is obtained by changing the sign of the…

Q: 1. a) Find parametric equations of the line of intersection of the planes 3x- 2y+z=0 and…

A: Given : equation of a plane, 3x-2y+z=08x+2y+z-11=0

Q: [3] 8. Let 72, s = 1, and t = a. Find scalars a, b, and c such that ar + b3 + ct = 0 [7 31 [5] b.…

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Q: 3.2.14. Fix 1 <p< oo. Given x, y E lP, prove that ||r+ yllp = ||x||, + ||y||p if and only if x = 0…

A: Let x,y∈lp where 1&lt;p&lt;∞. Suppose x=0, then x+yp=0+yp=yp=0+yp=xp+yp Suppose y=αx, where α is a…

Q: (A IF A 2 1 3 -9 | -3 and B- is (A.B) null matrix. (B) plot the polar graph v=5+3 (B-

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Q: nd the orthogonal trajectories of the family of confocal central conics given as: = 1 a² + à b² + à

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Q: Write an equation for the conic in the xy-plane for - ) 1 at e- 30°. 15 3x° + 42/3xy- 39y² – 360 - 0…

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Q: Part 3 of 6 Note that N dS = VG(x, y, z) dA, and recall that VG(x, y, z) = (curl F). NdS = (2yi + (y…

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Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: H.W. 2 Let 71 = -2 + 1li, 22 = 2 - i. Showing the details of your work, ind, in the form x + iy: %3D…

A: z1 = -2+11i z2 = 2-i (z1 - z2)2/16 = (-2+11i -(2-i))2/16 = (-4 + 12i)2/16 = (16 -96i -144)/16 (z1 -…

Q: Question 1. Show that, if u(r, y) = x²-y²+2x+1 and v(x, y) = 2ry+2y, then 4(z² +y² +2x+1) Gty2E+1) (…

A: Given, ux,y=x2-y2+2x+1,vx,y=2xy+2y Shows in the following that…

Q: The matrix A = 4 4 has a singular value decomposition A = UEVT where U = and 6. 0 0 6 0 0 0 and The…

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Q: Express In(3 + j4) to polar form. a) 1.857- 29.950 b) -1.857- 29.95° c) -1.85729.95° d) 1.85729.95°…

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Q: Find the decomposition of a(t) a = arT + așN into tangential and normal components for r(1) = (5t,…

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Q: Chapter 5, Reserve Problem 5/054 Determine the coordinates of the centroid of the shaded area. 1.5"…

A: To determine the coordinates of the centroid of the given shaded region.

Q: 1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

A: Given that A = xy i + yzj + zxk and find curlA and curlcurlA at point (1,2,-3). Here i attached…

Q: Find a parametric representation for the lower half of the ellipsoid 5x² + 4y2 + z² = 1.

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Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: Show that [0, o0) and [1, o0) are isometric.

A: We need to show that ,  [0 , ∞)  and  [1 , ∞) are isometric. We know that two metric spaces X and Y…

Q: A nondegenerate conic section of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 is a/an________ if B2 -…

A: A nondegenerate conic section of the form Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 is a/an________ if B2 -…

Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

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Q: Is it true or false that the coefficients of first order terms of the conic Ax? + Bry+ Cy² + Dx +…

A: Consider the provided question, To write the general second degree polynomial equation Ax2 + Bxy +…

Q: , a curve in the z-plane and a complex mapping w = f(z) are given. In each case, find the image…

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Q: o Let ã = (5,-2,-2) and 5= (-3, -3,0) ニ Show there ane scalars s and t so that -> sá + tb = -…

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Q: 2. 22 – x2 1 By sketching the traces on the ry-, rz- and yz-plane a.

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Q: 1. Classify the equations below according to the type : * i) Uxx- 2uxy – 2uy = 0 O hyperbolic O…

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Q: (ii) Prove that the product of matrices cos²0 Icos@sin0 cos@sin@] sin?e cos²p B = lcosøsing…

A: Given the matrix is A=cos2θcosθsinθcosθsinθsin2θB=cos2φcosφsinφcosφsinφsin2φ

Q: 1 5 -6 Let y = -1 , U1 = 7 4 -2 Compute the distance d from y to the plane in R' spanned by uj and…

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Q: Example 19-1. Given Uo = 3, U1 = 12, U2 = 81, U3 = 200, U4 = 100 and U = 8, find %3D %3D %3D %3D

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Q: 2. Thàngle LMN with vertices L(6, 6), M(8, 8), and N(8, 3): a) reflection in the linex = 5 b) 270°…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: Suppose that a, b, c € R are all nonzero. Find a QR-decomposition for Га 0 а] 0 c A = 0 b b а 0 0 if…

A: Consider the matrix A=a0a0cc0bba00, a,b,c∈ℝ and a,b,c≠0 with the vectors a1=a,0,0,aT,a2=0,c,b,0T,…

Q: Find the decomposition of a(t) a = arT + aŋN into tangential and normal components for r(t) = (5t,…

A: Given rt=&lt;5t,2t2,2t3&gt; at t=1        rt=5ti+2t2j+2t3k       r't=5i+4tj+6t2k…

Q: 1 1 1 Q2\ If Z = 2+j, Z, =-2+ j4 and Z3 evaluate z, in the form %3D Z, z, X +jy and in polar form.

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Q: 1 Let A = 2 -1 [1 find the singular value decomposition of A (i.e. A = USVT).

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Q: 12. Let # be the intersection of the planes 2g-ytz30 and a-2y+2=0 in R³ Find parametric equations…

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Q: Question 13 Find the cosine of the ngle betwoon the vectons ut,1.0 and v0,1,1) with respect to the…

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Q: Show that the “conic” x2 + 3y2 − 6x + 12y + 23 = 0 has no points.

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Q: 1234 5678 9 10 11 12 13 14 Find the coordinates of the image J (8, 7) after a reflection over the…

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Q: Let F: IR3 →IR3 is a diffeomorphism and M is a surface in IR3 , prove that the image F(M) is also a…

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Q: EXAMPLE 4 Find a parametric representation for the sphere x2 + y2 + z? = n².

A: Recall:    Spherical Coordinates:                   x=ρ sin ϕ cos θy=ρ sin ϕ sin θ z=ρ cos ϕ…

Q: Question 7. Consider the solid in ryz-space, which contains all points (r, y, z) whose z-coordinate…

A: Given equation of solid, 0≤z≤4-x2-y2 This is not a equation of sphere. Also, the solid is not a…

Q: 2: find the cofactors of given matrix sec30 100 37 sin240 cot30

A: solution :- Given matrix is -                  sec 30°10037 sin 240°Cot 30°So, Cij = Cofector of i…

Q: Q2: A parametric cubic curve passes through the points (1,1), (2,3), (3,4), (5,-2) which…

A: Given: A parametric cubic curve passes through the points (1,1),(2,3),(3,4),(5,2) at t=0.2,0.4,0.6,…