1. **Calculate** $-\frac{12}{5} + \frac{7}{8} - \frac{4}{9} + \frac{3}{5}$. Find common denominator, which is $\mathrm{lcm}(5,8,9) = 360$. $-\frac{12}{5} = -\frac{12 \times 72}{360} = -\frac{864}{360}$. $\frac{7}{8} = \frac{7 \times 45}{360} = \frac{315}{360}$. $-\frac{4}{9} = -\frac{4 \times 40}{360} = -\frac{160}{360}$. $\frac{3}{5} = \frac{3 \times 72}{360} = \frac{216}{360}$. Sum all: $-864 + 315 -160 + 216 = -493$. Result: $-\frac{493}{360}$ or approximately $-1.369$. 2. **Calculate** $\frac{1}{6} + \frac{3}{8} - \frac{5}{24}$. Common denominator $= 24$. $\frac{1}{6} = \frac{4}{24}$, $\frac{3}{8} = \frac{9}{24}$, $\frac{5}{24} = \frac{5}{24}$. Sum: $4 + 9 - 5 = 8$. Result: $\frac{8}{24} = \frac{1}{3}$. 3. **Calculate** $-\frac{5}{13} + \frac{7}{12} + -\frac{5}{13} \times \frac{5}{12} + -\frac{5}{17}$. Calculate product: $-\frac{5}{13} \times \frac{5}{12} = -\frac{25}{156}$. Common denominator for sums: $13, 12, 156, 17$; use $132$ or $1320$, pick $1320$. Convert each term: $-\frac{5}{13} = -\frac{5 \times 101.54}{1320} \approx -\frac{507.7}{1320}$, $\frac{7}{12} = \frac{7 \times 110}{1320} = \frac{770}{1320}$, $-\frac{25}{156} = -\frac{25 \times 8.46}{1320} = -\frac{211.5}{1320}$, $-\frac{5}{17} = -\frac{5 \times 77.65}{1320} = -\frac{388.25}{1320}$. Sum numerators: $-507.7 + 770 - 211.5 - 388.25 = -337.45$. Result: approximately $-\frac{337.45}{1320} \approx -0.256$. 4. **Calculate** $$\frac{2023}{2024} \times \left(\frac{2}{5}\right)^2 \times \frac{29}{25} \times \frac{2024}{2023}$$ Simplify $\frac{2023}{2024} \times \frac{2024}{2023} = 1$. Then $\left(\frac{2}{5}\right)^2 = \frac{4}{25}$. So expression becomes $$1 \times \frac{4}{25} \times \frac{29}{25} = \frac{4 \times 29}{25 \times 25} = \frac{116}{625}$$. 5. Solve for $x$ in: (a) $x - \frac{3}{10} = -0.28$ Convert $-0.28$ to fraction $-\frac{28}{100} = -\frac{7}{25}$. So $$x = -\frac{7}{25} + \frac{3}{10} = -\frac{7}{25} + \frac{15}{50} = -\frac{14}{50} + \frac{15}{50} = \frac{1}{50} = 0.02$$. (b) $\frac{2}{3}x + \frac{1}{5} = \left(\frac{7}{10}\right)^2 = \frac{49}{100}$ Subtract $\frac{1}{5} = \frac{20}{100}$: $$\frac{2}{3}x = \frac{49}{100} - \frac{20}{100} = \frac{29}{100}$$ Multiply both sides by $\frac{3}{2}$: $$x = \frac{29}{100} \times \frac{3}{2} = \frac{87}{200} = 0.435$$. (c) $$\left(-\frac{5}{4}\right)^7 \times \left(2x - \frac{1}{5}\right) = \left(-\frac{5}{4}\right)^8$$ Divide both sides by $$\left(-\frac{5}{4}\right)^7$$: $$2x - \frac{1}{5} = -\frac{5}{4}$$ Solve for $x$: $$2x = -\frac{5}{4} + \frac{1}{5} = -\frac{25}{20} + \frac{4}{20} = -\frac{21}{20}$$ $$x = -\frac{21}{40} = -0.525$$. 6. Geometry problem on lines $ab$ and $xy$ intersecting at $O$. (a) Find all supplementary (kề bù) adjacent angles to $\angle aOx$. These are $\angle xOb$ and $\angle bOa$ because adjacent angles on a straight line sum to 180°. (b) Given $\angle xOa = 65^\circ$, find $\angle xOb$. Since $\angle aOx$ and $\angle xOa$ are the same angle, $\angle xOb$ is supplementary to it. So $$\angle xOb = 180^\circ - 65^\circ = 115^\circ$$. 7. Rectangular prism $ABCD.EFGH$ with $AB=10$ cm (length), $EF=18$ cm (width), $CG=8$ cm (height). (a) Calculate lateral surface area (diện tích xung quanh): Lateral surface area $= 2 \times$ height $\times$ (length + width) $$= 2 \times 8 \times (10 + 18) = 16 \times 28 = 448 \text{ cm}^2$$. (b) Calculate volume: $$V = \text{length} \times \text{width} \times \text{height} = 10 \times 18 \times 8 = 1440 \text{ cm}^3$$. 8. Fish tank dimensions: height = 75 cm, length = 120 cm, width = 60 cm. (a) Glass area excluding top: Surface area excluding top = bottom area + 4 side areas Bottom = $120 \times 60 = 7200$ cm$^2$. Sides: 2 sides $= 2 \times 120 \times 75 = 18000$ cm$^2$, 2 sides $= 2 \times 60 \times 75 = 9000$ cm$^2$. Total glass area (no lid): $$7200 + 18000 + 9000 = 34200 \text{ cm}^2 = 3.42 \text{ m}^2$$. (b) Water volume = $6 \times 18$ liters $= 108$ liters = $108000$ cm$^3$. Volume $= \text{base area} \times \text{water height}$. Water height = $$\frac{108000}{120 \times 60} = \frac{108000}{7200} = 15 \text{ cm} = 0.15 \text{ m}$$. 9. A store buys 100 Sony TVs at 8400000 VND each. Sell 50 TVs at 15% profit + 150000 VND advertising each. Cost price per TV = 8400000. Sell price per TV in stage 1: $8400000 \times 1.15 + 150000 = 9660000 + 150000 = 9810000$ VND. Profit per TV stage 1: $9810000 - 8400000 = 1410000$ VND. Total profit stage 1: $50 \times 1410000 = 70500000$ VND. Sell 30 TVs at 9% discount + 200000 VND storage. Sell price per TV: $8400000 \times 0.91 - 200000 = 7644000 - 200000 = 7444000$ VND. Profit per TV stage 2: $7444000 - 8400000 = -956000$ VND (loss). Total loss stage 2: $30 \times 956000 = 28680000$ VND loss. Sell remaining 10 TVs at 12% discount + 200000 VND storage. Sell price per TV: $8400000 \times 0.88 - 200000 = 7392000 - 200000 = 7192000$ VND. Profit per TV stage 3: $7192000 - 8400000 = -1208000$ VND (loss). Total loss stage 3: $10 \times 1208000 = 12080000$ VND loss. Net profit after selling 90 TVs: $70500000 - 28680000 - 12080000 = 29740000$ VND profit. **Final answers:** 1) $-\frac{493}{360}$ 2) $\frac{1}{3}$ 3) Approx. $-0.256$ 4) $\frac{116}{625}$ 5a) $x = 0.02$ 5b) $x = 0.435$ 5c) $x = -0.525$ 6a) Adjacent supplementary angles: $\angle xOb$, $\angle bOa$ 6b) $\angle xOb = 115^\circ$ 7a) Lateral area = 448 cm$^2$ 7b) Volume = 1440 cm$^3$ 8a) Glass area no lid = 3.42 m$^2$ 8b) Water height = 0.15 m 9) Net profit after selling 90 TVs = 29740000 VND