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Home Question Bank Other Archive 2024 December 11

Other Questions from Dec 11,2024

Browse the Other Q&A Archive for Dec 11,2024, featuring a collection of homework questions and answers from this day. Find detailed solutions to enhance your understanding.

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Let \( P=\{a, b, c, d\}, Q=\{c, d, e, f, g\} \) and \( R=\{e, f, g, h, i, j, k\} \) Find: i) \( P \cap R \) ii) \( P \cup Q \) iii) \( Q \oplus R \) Find all values of \( h \) for which the set \( [a, b, c, d] \) is linearly independent. \( a=(1,2,-2,0,-1) \) \( b=(-3,0,1,3,-6) \quad c=(-1,1,2,-1, h) \quad d=(2,1,-3,-1,4) \) \( \left[\begin{array}{rrrr}1 & -3 & -1 & 2 \\ 2 & 0 & 1 & 1 \\ -2 & 1 & 2 & -3 \\ 0 & 3 & -1 & -1 \\ -1 & -6 & h & 4\end{array}\right] \) Calculate the eigen values and vectors \( A=\left[\begin{array}{cc}3 & -2 \\ 2 & 3\end{array}\right] \) What do we call it when there is scientific evidence demonstrating a plausible risk from a chemical, it must be further tested to prove that it is safe before it can continue to be used? Eutrophic Principle Precautionary Principle What do we call the process of examining evidence and linking a potential hazard to its harmful effects? Hazard assessment Eutrophic principle Given the vector space \( W \), find \( W^{\perp} \) \( V=\operatorname{span}[(1,-1,2,3),(3,-5,2,1),(2,6,0,3)] \) 4- Let \( \mathrm{A}=\{1,2,3\}, \mathrm{B}=\{\mathrm{X}, \mathrm{Y}, \mathrm{Z}\} \) and \( \mathrm{C}=\{\mathrm{P}, \mathrm{O}\}: \) a) Find the of following : \( \quad A \times B \times C= \) \( \begin{array}{l}A \times(B \times C)= \\ \\ (A \times B) \times C= \\ \text { b) What do you note about } A \times B \times C, A \times(B \times C) \text { and }(A \times B) \times C \\ \text { c) What is a relation between } n(A), n(B), n(C) \text { and } n(A \times B \times C)\end{array} \) 3) Determine if the columas of the Matrix span \( R^{4} \) \( A=\left[\begin{array}{ccccc}12 & -7 & 11 & -9 & 5 \\ -9 & 4 & -8 & 7 & -3 \\ -6 & 11 & -7 & 3 & -9 \\ 4 & -6 & 10 & 5 & 12\end{array}\right] \) A disadvantage of using water to suppress a fire is: A) Damages building contents, B) Conducts electricity as a stream, C) Flammable oils float on surface and continues D) All the above 1. Estimate daily energy needs for an active 60 kg woman and a 70 kg sedentary man.
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