Explanation

(a)(i) How fast a reaction can take place.

(ii) Collision theory states that the reactant molecules must collide with one another before forming the product. The number of collisions is directly proportional to the rate of reaction. This value of rate of reaction is however limited by the number of molecules attaining the activation energy and having appropriate orientation of the molecules. Increase in temperature only favours endothermic process and low temperature will favour the exothermic process. Low temperature however slows the rate of reaction and therefore catalyst is applied.

(b)(i) 2H\(_2\)O\(_{2(l)}\) \(\to\) 2H\(_2\)O\(_{(l)}\) + O\(_{2(g)}\)

(ii) Thermodynamically, the decomposition of hydrogen peroxide is spontaneous. When hydrogen peroxide is put in a conical flask, nothing seem to happen. However. the addition of hydrogen peroxide to a little amount of manganese(IV) oxide (MnO\(_2\)) generates effervescence and a gas is vigorously given off. The reaction of MnO\(_2\) on the decomposition of hydrogen peroxide is catalystic.

(iii) Energy profile.

(c)(i) Certain endothermic processes can be exothermic at a certain condition of temperature.

Correct Answer: A. frequent opposition by the landlords

Explanation

P: (x, y) → (2x+3y, 3x - y)

\(\begin{pmatrix} x\\ y \end{pmatrix}\) → \(\begin{pmatrix} -3x & 6y \\ 4x & + y \end{pmatrix}\)

= \(\begin{pmatrix} -3 & 6 \\ 4 & + 1 \end{pmatrix}\) \(\begin{pmatrix} x\\ y \end{pmatrix}\)

P = \(\begin{pmatrix} -3 & 6 \\ 4 & + 1 \end{pmatrix}\)

Q: (x, y) → (2x-3y, -4 - 6y)

\(\begin{pmatrix} x\\ y \end{pmatrix}\) → \(\begin{pmatrix} 2x & -3y \\ -4x & -6y \end{pmatrix}\)

= \(\begin{pmatrix} 2 & -3 \\ -4 & -6 \end{pmatrix}\) \(\begin{pmatrix} x\\ y \end{pmatrix}\)

Q = \(\begin{pmatrix} 2 & -3 \\ -4 & -6 \end{pmatrix}\)

(b) \(\begin{pmatrix} 2 & -3 \\ -4 & -6 \end{pmatrix}\) \(\begin{pmatrix} -2 \\ -3 \end{pmatrix}\)

= \(\begin{pmatrix} 2[-2] & -3[-3] \\ -4[-2] & -6[-3] \end{pmatrix}\)

= \(\begin{pmatrix} -4 & +9 \\ 8 & 18 \end{pmatrix}\)

= \(\begin{pmatrix} 5 \\ 26 \end{pmatrix}\)

: The image of (-2,-3) is (5,26)

(c) PQ = \(\begin{pmatrix} -3 & 6 \\ 4 & 1 \end{pmatrix}\) \(\begin{pmatrix} 2 & -3 \\ -4 & -6 \end{pmatrix}\)

\(\begin{pmatrix} -3[2] + 6[-4] & -3[-3] + 6[-6] \\ 4[2] + 1[-4] & 4[-3] + 1[-6] \end{pmatrix}\)

= \(\begin{pmatrix} -6 - 24 & 9 - 36 \\ 8 - 4 & -12 - 6 \end{pmatrix}\) = \(\begin{pmatrix} -30 & -27 \\ 4 & -18 \end{pmatrix}\)

= PQ: (x,y) → (-30x - 27y, 4x - 18y)

(d) \(\begin{pmatrix} -30 & -27 \\ 4 & -18 \end{pmatrix}\) \(\begin{pmatrix} 1 \\ 4 \end{pmatrix}\)

= \(\begin{pmatrix} -30[1] & + [-27][4] \\ 4[1] & + [-18][4] \end{pmatrix}\)

= \(\begin{pmatrix} -30 & -108 \\ 4 & -72 \end{pmatrix}\) = \(\begin{pmatrix} -138 \\ -68 \end{pmatrix}\)

: Image of the point (1,4) is (-138,-68)

(e) T = \(\begin{pmatrix} cos 225° & -sin 225 \\ sin 225° & cos 225° \end{pmatrix}\)

= \(\begin{pmatrix} -√2/2 & √2/2 \\ -√2/2 & -√2/2 \end{pmatrix}\) \(\begin{pmatrix} -√2 \\ 2√2 \end{pmatrix}\)

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

: The image of P\(^1\) is (3,-1)

Correct Answer: C. factor

Correct Answer: A. 2

Explanation

5 1 6 2_seven

-2 6 4 4_seven

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2 2 1 5

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the missing number is 2

Correct Answer: A. Centripetal forces only

Correct Answer: B. I and III only

Correct Answer: B. reduced to a quarter

Correct Answer: D. climate conditions of the different parts of the country

Correct Answer: C) Gills

Explanation

Tadpoles are the larval form of frogs and they undergo metamorphosis to become adult frogs. Respiration is the process of taking in oxygen and releasing carbon dioxide. The question is asking how tadpoles respire. The options given are lungs, nostrils, gills, spiracles, and siphon. Lungs are organs used for breathing air, while nostrils are openings in the nose used for breathing. Spiracles are openings on the body of certain insects used for breathing air. Siphons are tube-like structures used for drawing in water. The correct answer is gills. Tadpoles respire by absorbing oxygen from the water through their gills and releasing carbon dioxide. Gills are specialized organs that are used for breathing underwater. They are found in many aquatic animals, including fish and amphibians like tadpoles. It is important to note that as tadpoles metamorphose into adult frogs, they develop lungs and begin to breathe air. This allows them to live both on land and in water. In summary, tadpoles respire with gills, which are specialized organs that allow them to breathe underwater. As they metamorphose into adult frogs, they develop lungs and can breathe both on land and in water.