4. 設二階實係數方陣 a b A c d = 滿足行列式det( ) 1 A = ,O 是坐標平面的原點,對於所有的正整數n,平 面上的點 ( , ) P x y n n n 滿足 1 0 n n n x A y = 。若 1 2 OP OP = =1,試證明對於所有的正整數n, 1 OPn = 。(9 分)
3. 試證明:對任意的實數 ,,,都有√ + + + √ + + ≥ &3 + + + ,並說 明等號成立的充要條件。(9 分)
2. 對於正整數 n,函數 f (n)定義為 f (n) = [ ] n n ,其中符號[ ]為高斯符號。 例如:f (7) = 7 [ 7] = 7 2 = 3。
(2) 在所有滿足 n ≤ 2025 的正整數 n 中,求使得 f (n) > f (n + 1) 的 n 共有幾個? (5 分)
There are some simple tips for what to do before traveling internationally. First, the validity of your passport can be an easy oversight. A passport validity of 10 years can make people complacent, forgetting that it actually requires renewing. Many countries won’t allow entry if your passport has less than 6 months remaining. A good rule of thumb is to ensure your passport is valid when booking your flight.
Additionally, check in advance if you need a visa. Arriving for your flight without the necessary visa can lead to being denied boarding, especially if you can’t apply for one on arrival. US and UK passport holders can travel to many countries without a visa or receive one upon arrival. However, entry requirements vary, so thorough research is essential.
Investing time in researching your destination is also important to optimize your experience. While spontaneous travel seems fun, being aware of the nuances of your destination country can be more practical. This includes understanding differences in language, culture, and laws. For instance, chewing gum is illegal in Singapore, feeding pigeons is prohibited in Venice, and riding a cow while intoxicated is not allowed in Scotland. Knowing them ahead of time can keep you out of trouble.
80 Which of the following is mentioned as an illegal activity in a foreign country? (A) Feeding pigeons in Venice (B) Riding a bicycle on sidewalks in Scotland (C) Eating on the street in Singapore (D) Taking pictures of US government buildings
79 What does ‘them’ in the last sentence refer to? (A) destinations (B) countries (C) laws (D) passports
78 In the passage, what does the word ‘nuances’ most closely mean? (A) Legal differences (B) Subtle differences (C) Cultural variations (D) Major contrasts