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question:Which of the following represent the same set? ( ) A: M={(1,2)}, N={(2,1)} B: M={1,2}, N={(2,1)} C: M=emptyset, N={emptyset} D: M={x | x^2-3x+2=0}, N={1,2}
answer:Solution: A. (1,2) and (2,1) represent two different points, therefore M neq N, so this option is incorrect; B. M has two elements, 1 and 2, while N has one element, the point (2,1), therefore M neq N, so this option is incorrect; C. The set M is an empty set, while the set N contains one element, the empty set, therefore M neq N, so this option is incorrect; D. Solving x^2-3x+2=0 yields x=1,2, therefore M={1,2}=N, so this option is correct. Hence, the correct choice is boxed{D}. This question examines the concept of set equality and the composition of set elements.
question:Hey Mike! I just saw the email from HQ about the new project, and I’m SO EXCITED!!! We need to nail down the PM2.5 levels, dude. It’s gonna be epic! What do you think about our roles? I was thinking you could handle the data analysis and I’ll take care of the field research. Let me know what you think. Can’t wait to get started! Peace out, Sarah
answer:Dear Mike, I hope this message finds you well. I have just reviewed the email from Headquarters regarding our new project, and I am quite enthusiastic about the opportunities it presents. One of our primary objectives will be to accurately determine the PM2.5 levels, which is a critical aspect of the project. I have been considering our respective roles and responsibilities. Given your expertise, I believe it would be most effective for you to manage the data analysis component, while I could focus on conducting the field research. I value your input on this proposed division of tasks and am open to any suggestions you might have. I am eager to begin this project and look forward to your thoughts. Best regards, Sarah
question:In the Cartesian coordinate system, the coordinates of point P(2,1) with respect to the y-axis symmetric point P' are ( ). A: (-2,-1) B: (1,2) C: (2,-1) D: (-2,1)
answer:To find the coordinates of point P', which is symmetric to point P(2,1) with respect to the y-axis, we need to reflect P across the y-axis. Reflecting a point across the y-axis changes the sign of its x-coordinate while keeping its y-coordinate the same. Therefore, the transformation can be described as follows: - The x-coordinate of P is 2. Reflecting across the y-axis changes this to -2. - The y-coordinate of P is 1. Reflecting across the y-axis does not change this value. Thus, the coordinates of P' are left(-2,1right). Therefore, the correct answer is boxed{D}.
question:A group of friends decide to explore the woods near their hometown, with long-abandoned, mysterious government research facilities, and strange occurrences. How do you suggest I start the story? Consider their personalities too.
answer:What a great premise for a story. To begin, let's set the tone and introduce your characters in a way that makes the reader curious about the mysterious woods and the research facilities. You could start with a casual gathering of friends, perhaps at a local diner or someone's backyard, where they discuss the rumors and urban legends surrounding the abandoned facilities. This will allow you to showcase their personalities and dynamics. Imagine your group of friends consisting of a mix of skeptics and believers. There's Emily, the history buff who's researched the facilities and is convinced that there's more to the story than what's been told. Then there's Matt, the thrill-seeker who's always up for a challenge and is drawn to the danger and mystery of the woods. Sarah, on the other hand, is more cautious, but her curiosity gets the better of her. Jack, the class clown, is along for the ride, but his jokes and teasing hide a deeper unease. As they discuss their plans, you could sprinkle in hints about the strange occurrences in the woods, such as unexplained lights, eerie sounds, or sightings of strange creatures. This will create tension and foreshadow the events that will unfold. Here's a possible opening scene: The sun was setting over the small town, casting a warm orange glow over the group of friends gathered in Emily's backyard. They sat around a picnic table, surrounded by empty pizza boxes and soda cans, their conversation fueled by a mix of excitement and apprehension. I'm telling you, it's not a good idea, Sarah said, shaking her head. We don't know what's out there. Come on, it'll be fun, Matt replied, grinning. We can't let a few rumors scare us off. Emily leaned forward, her eyes shining with enthusiasm. I've researched the facilities, guys. There's definitely something weird going on. We could uncover something big. As they talked, Jack cracked jokes and teased his friends, but his eyes betrayed a flicker of unease. Despite their differences, they were all drawn to the mystery of the woods, and the abandoned facilities seemed to be beckoning them. With this opening scene, you've introduced your characters, set the tone, and hinted at the mysteries that lie ahead. Now, you can start to build tension and suspense as they embark on their journey into the unknown.