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Maths-

General

Easy

Question

If I = $open square brackets table row 1 0 row 0 1 end table close square brackets$ , J = $open square brackets table row 0 1 row cell negative 1 end cell 0 end table close square brackets$ and B = $open square brackets table row cell cos invisible function application theta end cell cell sin invisible function application theta end cell row cell negative sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets$ , then B equals

I cosθ + J sinθ
I sinθ + J cosθ
I cosθ – J sinθ
– I cosθ + J sinθ

The correct answer is: I cosθ + J sinθ

I cos q + J sin q = $open square brackets table row cell cos invisible function application theta end cell 0 row 0 cell cos invisible function application theta end cell end table close square brackets$ + $open square brackets table row 0 cell sin invisible function application theta end cell row cell negative sin invisible function application theta end cell 0 end table close square brackets$
= $open square brackets table row cell cos invisible function application theta end cell cell sin invisible function application theta end cell row cell negative sin invisible function application theta end cell cell cos invisible function application theta end cell end table close square brackets$ = B

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If A‘ is the transpose of a square matrix A, then

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parallel

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The value of $open vertical bar table row cell sin invisible function application theta end cell cell cos invisible function application theta end cell cell sin invisible function application 2 theta end cell row cell sin invisible function application open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses end cell cell cos invisible function application open parentheses theta plus fraction numerator 2 pi over denominator 3 end fraction close parentheses end cell cell sin invisible function application open parentheses 2 theta plus fraction numerator 4 pi over denominator 3 end fraction close parentheses end cell row cell sin invisible function application open parentheses theta minus fraction numerator 2 pi over denominator 3 end fraction close parentheses end cell cell cos invisible function application open parentheses theta minus fraction numerator 2 pi over denominator 3 end fraction close parentheses end cell cell sin invisible function application open parentheses 2 theta minus fraction numerator 4 pi over denominator 3 end fraction close parentheses end cell end table close vertical bar$ is :

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Physics-General

If A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, then $left parenthesis A cross times B right parenthesis intersection left parenthesis B cross times C right parenthesis$ is equal to

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