(s+1)2 f L-²[F(s)] = f(t), evaluate f(0) given by the expression F(s) s(s+2)(s²+2s+2) Express your answer in two decimal place number.

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A: The solution is given as

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A: We will use definition of Laplace transformation to solve this problem.

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A: this question related to ring theory and group theory.

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A: Let G be a group of prime order p. To prove G is cyclic.

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A: field D=6ρsin12ϕ ap + 1.5ρcos12ϕ aϕ C/m2 here ∇ = aρ ddρ + aϕddϕ+azddz Divergence = ∇·D ∇·D=…

Q: Q3: (A) Prove that 1. There is no simple group of ord er 200. 2. Every group of index 2 is normal.

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Q: Exercise 6.3.12. Suppose G is a group, a, b e G such that gcd(la\, [b|) = 1. Prove (a) n (b) = {e}.

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A: According to guidelines here solution of only firt question

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Q: Question 3.1. Let's think of the set of n-by-n matrices as R by using the matrix entries as…

A: Given :   D⊂ℝn2Let  A∈DThen  A = (a11 , a12 , ....... a1n , a21 , a22 , ....... , a2n , ...... an1 ,…

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A: We use properties of matrices.

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Q: (A) Prove that 1. There is no simple group of order 200. 2. Every group of index 2 is normal.

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A: As per the policy of bartleby the provisions is to solve only one question at a time

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Q: السعلهلتمـِxله ملتلعللمو ) محلموكلوفحلرللت )رههد x^(5- )x = )ه ,4¢x

A: The given P.D.E is                              utt=16uxxu0,t=u5,t=0, utx,0=0   ux,0=x25-x To find:…