Explanation

(a) \(m \begin{pmatrix} 2 \\ 1 \end{pmatrix} + n \begin{pmatrix} -1 \\ 2 \end{pmatrix} = \begin{pmatrix} 5 \\ -4 \end{pmatrix}\)

\(2m - n = 5 ...(1)\)

\(m + 2n = -4 ... (2)\)

\((1) \times 2 : 4m - 2n = 10 ... (3)\)

\((2) + (3) : 5m = 6 \implies m = \frac{6}{5}\)

\(2(\frac{6}{5}) - n = 5 \implies n = \frac{12}{5} - 5 = \frac{-13}{5}\)

\(\therefore (m + n) = (\frac{6}{5} + \frac{-13}{5}) = -\frac{7}{5}\).

(b) A(-1, 3) = (-i + 3j)

B(2, -1) = (2i - j)

\(\overrightarrow{AB} = \overrightarrow{OB} - \overrightarrow{OA}\)

\(\overrightarrow{AB} = \begin{pmatrix} 2 \\ -1 \end{pmatrix} - \begin{pmatrix} -1 \\ 3 \end{pmatrix}\)

= \(\overrightarrow{AB} = \begin{pmatrix} 3 \\ -4 \end{pmatrix}\)

\(|\overrightarrow{AB}| = \sqrt{3^{2} + (-4)^{2}} = 5\)

Unit vector parallel to AB = \(\frac{1}{5} \begin{pmatrix} 3 \\ -4 \end{pmatrix}\)

\(\overrightarrow{OA} + \overrightarrow{AC} = \overrightarrow{OC}\)

\(\overrightarrow{AC} = \overrightarrow{OC} - \overrightarrow{OA}\)

= \(\begin{pmatrix} 5 \\3 \end{pmatrix} - \begin{pmatrix} -1 \\ 3 \end{pmatrix}\)

= \(\begin{pmatrix} 6 \\ 0 \end{pmatrix}\)

\(|\overrightarrow{AC}| = 6\)

Unit vector parallel to AC = \(\frac{1}{6} \begin{pmatrix} 6 \\ 0 \end{pmatrix}\)

(ii) Let the angle BAC = \(\theta\)

\(\overrightarrow{AB} \cdot \overrightarrow{AC} = |\overrightarrow{AB}||\overrightarrow{AC}| \cos \theta\)

\((3i - 4j) \cdot (6i + 0j) = |3i + 4j||6i + 0j| \cos \theta\)

\(18 = 5 \times 6 \times \cos \theta \implies \cos \theta = \frac{18}{30} = 0.6\)

\(\theta = \cos^{-1} (0.6) = 53.1°\)

Correct Answer: C. 1987

Correct Answer: C) Ecosystem

Explanation

An ecosystem is a group of populations of different species that interact with one another through trophic (feeding) and spatial relationships. In simpler terms, it is a community of living organisms (plants, animals, and microbes) in a particular habitat, along with the nonliving components of that environment (such as air, water, and soil). Option A, City, is not the correct answer because it refers to a human settlement and does not involve interactions between different species. Option B, Community, is close but not quite right. While it refers to a group of populations of different species, it does not necessarily involve interactions through trophic and spatial relationships. Option C, Ecosystem, is the correct answer. It encompasses all the living organisms in a particular environment, as well as the nonliving components that shape that environment. Ecosystems can range from small, localized areas (such as a pond or a meadow) to large, global systems (such as the ocean or the atmosphere). Option D, Niche, refers to the specific role that a species plays within an ecosystem. While niches are important for understanding how different species interact with one another, they do not encompass the entire system of interactions that make up an ecosystem. In summary, the correct answer to this question is Option C, Ecosystem, because it best describes a group of populations of different species interacting through trophic and spatial relationships.

Correct Answer: A. Dumping

Correct Answer: D. Q. 2:255

Correct Answer: D. feeling ashamed for the betrayal

Correct Answer: A) involve chemical transmission

Explanation

The question is asking about the similarities between the nervous and hormonal systems. The options are given as follows: involve chemical transmission, have widespread effects, shed chemicals into the bloodstream, and evoke rapid response to eliminate response. The correct answer is option A: involve chemical transmission. Both the nervous and hormonal systems use chemicals to transmit messages or signals throughout the body. In the nervous system, neurons use chemical messengers called neurotransmitters to send signals between themselves and to other cells, while in the hormonal system, glands secrete hormones into the bloodstream to carry signals to different parts of the body. While both systems involve chemical transmission, there are some differences between them. For example, the nervous system is faster and more specific in its responses, while the hormonal system is slower and more widespread in its effects. Additionally, the nervous system can respond to immediate changes in the environment, while the hormonal system is more involved in long-term regulation and maintenance of bodily functions. Overall, understanding the similarities and differences between the nervous and hormonal systems is important for understanding how the body communicates and regulates its various functions.

Correct Answer: B. 2

Correct Answer: B. warehousing

Correct Answer: B. 0.896dm³