prove that go is a tensor
Q: Prove that matrix multiplication is associative. Show that the product of two orthogonal matrices is…
A: The objective of the question is to prove two properties of matrices: the associativity of matrix…
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Q: Given u x v = (3,-4,-3), find (ü - 3) × (u + 2u). X
A: The cross product of two vectors is given asNote:The cross-product of vector with itself is zero,…
Q: Find the principal invariants, principal values and principal directions of the order tensor T,…
A: The tensor given in the question is T=3-10-130001 This is a symmetric tensor. TT=T Let us calculate…
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Q: A vector field v is expressed in spherical coordinates as: v (r,θ,φ) = 2r cos θ er − r sin θ eθ…
A: To calculate the curl of a vector v(r,θ,φ)=vr er+vθ eθ+vφ eφ , we need to compute the determinant of…
Q: L,, Ly] = L,Ly – LyL = ihL, %3D %3D
A: We know, Lx^=y^pz^-z^py^Ly^=z^px^-x^pz^Lz^=x^py^-y^px^
Q: A four vector [A] and a tensor [B] are defined by: [A] = (-2, 7, 1,3) 1 3 -5 7 0 2 0 -1 5 5 2 6 -3…
A: given information=(-2 ,7, 1 3)
Q: A particle of mass m slides under the gravity without friction along the parabolic path y = a x²…
A: Introduction: Lagrangian is a quantity that describes a physical system's state. Just the kinetic…
Q: A A T4!= "T7-"T7= "77
A: The angular momentum of x and z component is defined as…
Q: Suppose that A,, is a covector field, and consider the object Fμv=O₁ Av - O₂ A₁. (a) Show explicitly…
A: The objective of the question is to prove that the definition F = ∇A - ∇A, which uses the covariant…
Q: Solve with explanation and calculation
A: By multiplying normal vector by -1 doesn't change anything for the plane.you can also reduce the…
Q: Find the mass of the lamina described by the inequalities x 20 and 7<y 37+V 49-x, given that its…
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Q: Suppose that A,, is a covector field, and consider the object Fμ = 0μA, O₂ A₁. (a) Show explicitly…
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Q: gradient vector field Vf
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Q: Obtain the law of transformation of the (four-)gradient of a contravariant vector and verify that it…
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Q: Prove the triple product identity Ax(B×C)= B(A·C)-C(A·B).
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Q: Suppose the following three conditions are satisfied: (i) v1, v2, 03, w are linearly independent.…
A: Option b and c are the correct answer w→ is the scalar multiple of z→ Span v1→,v2→,v3→,w→, z→=span…
Q: Which of the following is conserved if the Lagrangian of the system is given as: 1 L=-m(x° + y*…
A: If the Lagrangian of the system is given, then the Lagrange's equation is defined as follows:
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- I need the answer as soon as possibleEx.6. If A; is a covariant tensor of the second order and Bi, C' are contravariant vectors; prove that A;¡BiC' is an invariant.Obtain the inertia tensor of a system, consisting of four identical particles of mass m each, arranged on the vertices of a square of sides of length 2a, with the coordinates of the four particles given by (±a, ta, 0). Y m (-a,a) X (-a,-a). m O m (a,a) (a,-a)
- Express the Lagrangian for a free particle moving in a plane in a plane polar coordinates. From this proves that, in terms of radial and tangential components, the acceleration inpolar coordinates isa = (¨r − rθ˙2) er + (rθ¨ + 2 r˙ θ˙) eθ(where er and eθ are unit vectors in the positive radial and tangential directions).1. Consider a vertical plane in a constant gravitational field. Let the origin of a coordinate system be located at some point in this plane. A particle of mass m moves in the vertical plane under the influence of gravity and under the influence of an addition force f = -Ar"- directed toward the origin (r is the distance from the origin; A and a [#0 or 1] are constants). Choose appropriate generalized coordinates, and find the Lagrangian equations of motion (don't solve it). Is the angular momentum about the origin conserved? Explain.Particle A lies on the xy plane and is acted on by the three forces shown. Find the resultant of the three forces. Also find the direction cosines of the resultant.
- For vector field v(x, y) = (-xy, y), find all points P such that the amount of fluid flowing in to Pequals the amount of fluid flowing out of P. Select the correct answer below: O At all points P O At all points P, where y s0 O At all points P, where y = 1 O At all points P, where y = xFind the commutatorSketch how water curls down a sink, say, in clock-wise rotation. Draw the resulting vector of the curl-operator applied on this water flow.
- Show that the directions of the isoline and the gradient line at any given points in a scalar field are orthogonal to each other.Send AnswerFor each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ∇f=F). F(x,y)=(−3siny)i+(10y−3xcosy)j