Explanation

1 Peter 5:1-11 (a)

(i) Peter urged elederly brethren to tend the flock of God that is in their charge not by constraint but willingly.

(ii) They should not do it for shameful gain but eagerly.

(iii) Not as domineering over those in their charge but being examples to the flock.

(iv) The younger brethren should be subject to the elders.

(v) They should clothe themselves with humility towards one another.

(vi) For God opposes the proud, but gives grace to the humble.

(vii) All Christians should humble themselves under the mighty hand of God that in due time, He may exalt them.

(viii) They should cast all their anxieties on him, for He cares about them.

(ix) He urges them to be sober, and watchful since Satan, roaring like lion, is seeking whom to devour.

(x) They should resist the devil firmly in their faith.

(xi) Since their brethren, throughout the world, face the same sufferings.

(xii) In the end, the Lord God will himself restore, establish and strengthen them.

(b) The causes of conflict among Christians:

(i) Covetousness/ greed.

(ii) Power/position.

(iii) Love of money

(iv) Criminal acts.

(v) Idolatrous practices.

(vi) Ostentatious.living

(vii) Doctrinal differences

(viii) Apostasy

(ix) Envy/Jealousy

(x) Fornication/adultery

(xi) Lack of love

(xii) Bribery and corruption in the Church.

Correct Answer: A. Loses electrons

Explanation

When a substance is oxidized, it loses electrons. Oxidation is a chemical reaction that involves the moving of electrons. Specifically, it's a process that involves the substance losing electrons. This is an old definition of oxidation, based on the oxygen's role in reactions. The modern definition of oxidation involves an increase in oxidation state by a molecule, atom, or ion.

Correct Answer: C. continuous variation

Explanation

(a)(i) The matrix of rotation of point anticlockwise through angle 60° about the origin is given by:

\(M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} = \begin{pmatrix} \cos 60° & -\sin 60° \\ \sin 60° & \cos 60° \end{pmatrix}\)

= \(\begin{pmatrix} \frac{1}{2} & \frac{-\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2} \end{pmatrix}\)

(ii) Using the transformation,

\(T :P \to MP\) or \(T : \begin{pmatrix} x \\ y \end{pmatrix} \to \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)

\(T : \begin{pmatrix} 3 \\ 5 \end{pmatrix} \to \begin{pmatrix} \frac{1}{2} & \frac{-\sqrt{3}}{2} \\ \frac{\sqrt{3}}{2} & \frac{1}{2} \end{pmatrix} \begin{pmatrix} 3 \\ 5 \end{pmatrix}\)

Image of P, P' = \(\begin{pmatrix} \frac{3 + 5\sqrt{3}}{2} \\ \frac{3\sqrt{3} - 5}{2} \end{pmatrix}\)

(b) \(T : \begin{pmatrix} x \\ y \end{pmatrix} \to \begin{pmatrix} 2x + 3y \\ 3x - y \end{pmatrix} = \begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix}\)

(i) \(N = \begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix}\)

(ii) \(N^{2} + aN + bI = 0\)

\(\begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix} ^{2} + a \begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix} + b \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\)

\(\begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix} \begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix} + a \begin{pmatrix} 2 & 3 \\ 3 & -1 \end{pmatrix} + b \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\)

\(\begin{pmatrix} 4 + 9 & 6 - 3 \\ 6 - 3 & 9 + 1 \end{pmatrix} + \begin{pmatrix} 2a & 3a \\ 3a & -a \end{pmatrix} + \begin{pmatrix} b & 0 \\ 0 & b \end{pmatrix} = \begin{pmatrix} 0 & 0 \\ 0 & 0 \end{pmatrix}\)

Adding corresponding elements of each matrix,

\(13 + 2a + b = 0 \implies 2a + b = -13 ... (1)\)

\(3 + 3a = 0 \implies 3a = -3 ; a = -1\)

\(2(-1) + b = -13 \implies -2 + b = -13\)

\(b = -13 + 2 = -11\)

\(\therefore a = -1 ; b = -11\)

Correct Answer: C. each participating atom contributes one electron

Correct Answer: B. wife

Correct Answer: B. varying magnetic field

Correct Answer: D. produce one main commodity

Correct Answer: D. Salih (A.S).

Correct Answer: C. carrier