According to Edwin Hubble our Universe is expanding because he noticed that other galaxies are moving away from us. But then how Andromeda galaxy will collide with Milky Way in ~4.5 billion years, as it should also move away from us?     I am some bit confused, please help me.
Hubble's law says that the universe is expanding. How come the Milky Way and the Andromeda galaxies are on a collision course? How will they end up colliding with each other?
I am non-EU citizen working in Germany. Can I travel to UK without a visa? How to make Stack Overflow tell you about a new question with certain tag(s) the second it is asked? Short Story/Novella in Which People Living in What they Think is Small Town Fifties America Find Look Magazine and Don't Recognize Anything in It This is probably from the mid-to-late fifties.  It involved families living in what seemed to be normal, small town America of the time.  But two boys found in a garbage dump or in a nearby landfill a copy of "LOOK" magazine from their time period (1955? 1957?).  Their problem was that they and their families didn't recognize any of the people or events that were reported in the magazine.    The tone of the articles in the magazine matched their actual lives in that the magazine reported world events, trouble spots, celebrities, politics, and had advertisements for cigarettes and TVs, etc. but the facts were completely different. I think the magazine was a magazine from 'real' America and they were living in a 'fake' America, i.e., they had been brought up in a separate isolated environment with everything different but now had found something from the 'real' world. The tone of the story was that they were never supposed to know about any of this. Maybe, just maybe, part of it was a story about Marilyn Monroe but none of the people had ever heard of her. I can't remember much more than that but I have a nagging thought that they were part of some controlled environment experiment by the US Military. Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$ Basis step has already been completed. I've started off with the inductive step as just $n=k+1$, trying to involve $f(k)$ into it so that the left over parts can be deducible to be divisible by $x^2$ but getting stuck on this inductive step. Is this a dismissal by hit wicket? Consider the following situation,     A batsman's bat breaks while hitting the ball after which a piece of the   bat flies in the air, hits the stumps and the bails fall down.   Is this a dismissal by hit wicket? Passive aggressive people will sometimes veil insulting, critical, derogatory or generally aggressive comments with humor. The patina of humor makes the comment seem like a joke, not to be taken seriously, all in good fun, and it safeguards the aggressive person. If someone gets offended, they are being too serious, can't take a joke, and so they cannot voice their upset without seeming to be the one escalating the situation, when in fact it was the aggressor who did that.   This behavior seems to lie on a spectrum. On one side are comments which are simultaneously aggressive and genuinely funny (though of course both, especially the latter, are fairly subjective). On the other side would be lame attempts at the behavior, something like "you are fat!... just joking!" in which nothing in the tone or delivery signals a register of humor. In the middle of the spectrum, I imagine, are aggressive statements genuinely delivered as jokes. Their register signals that they are jokes, but they are aggressive rather than funny. They are aggressive comments masquerading as jokes.      A friend once called this "joking on the square", but I have never heard or seen this phrase. This type of comment is both pervasive and psychologically subtle and in my experience there is often an exact word describing such things. If not a word, is there an astute phrase which cuts to the heart of this? Let $S=\{1,2,3,4,\dotsc,N\}$ and $X=\{ f: S \rightarrow S \mid x < y \Rightarrow f(x)\leqslant f(y)\}$. Then $|X|$ is equal to what? Is the $ L^{p}$$[0,1]$ norm continuous in p? I ran into the following problem when I was doing my homework, and I have no thoughts on where I should start with:  (1) If $f\in L^{2}$, show that $\displaystyle \lim_{p \rightarrow 1^{+}}\int_{[0,1]}|f|^{p}=\int_{[0,1]}|f|$  (2) If $0&lt;p$, show that $\displaystyle \lim_{q\rightarrow p^{-}}||f||_{q}=||f||_{p}$  My first thought was Generalized LDCT, but it didn't seem to work. I also made some other attempts but none of them were successful... Can anybody give me some hints on how I should look at this question?  Also, I know if $p\rightarrow\infty$ then $||f||_{p}\rightarrow||f||_{\infty}$ on $[0,1]$, but does similar continuity in p holds for other $L^{p}[0,1]$ norms in general?  Thank you!  Edit:   Sorry if I did not make it clear enough in the question. All $L^{p}$ refers to $L^p[0,1]$.  The first question is found  (thanks to t.b.), but the second question remains, mainly because $f$ is not guaranteed to be in any $L^{p}$. Earlier, I voted to close  as off-topic.  The question has since been closed.  There is an , but it didn't show up in the list when I selected "off-topic".  The options were:   Meta Stack Overflow Server Fault Super User Webmasters Programmers   Questions:   Should Wordpress appear in this list? Are there any other sites that should appear in the list?   Should all non-beta sites appear in that list by default? I'm looking for one word which describes what a student who missed classes needs to do Tsunami dampening mechanisms Encouraged by the zeitgeist let me ask the following:  Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it reaches the coast itself?  The following picture comes to mind. We have some device which is small enough to be mounted on a buoy. An array of such buoys can be anchored some distance off the coastline, controlled by computers which are linked into the global tsunami warning network. This setup is quite feasible given what a cell phone can do today.  On the detection of an oceanic earthquake or other tsunami generating event (such as a piece of the Rock of Gibraltar falling into the sea) and given present environmental conditions one can calculate the expected path of the tsunami and its intensity. If a TDS (Tsunami Dampening System) of the type I describe above happens to be deployed in range of the tsunami, all relevant information is conveyed to the TDS controllers by the global tsunami warning system. All this happen in a matter of moments.  This leaves plenty of time (25min - 2hr) for the devices in the TDS array to be activated and to do their job. The question in this case would be - what form could such devices take? Perhaps mini-turbines which could dissipate the incoming energy into the ocean by first converting it to electrical energy.  Any such undertaking involves physical estimates for the size and shape of such an array, the precise capabilities of each device, etc. Many of these concerns involve simple physical questions.  Can you come up with the details of such a system or alternatively outline your own design? If you think that this idea would never work in the first place - for technological, physical or some other reasons - please explain what you think would be the prime obstacle and why? If $\cot A+\cot B+\cot C=\sqrt3$ then prove that the triangle is equilateral triangle.   Trial: I can counter check that this is true as $\cot 60+\cot 60+\cot 60=3 \frac{1}{\sqrt3}=\sqrt3$.Here I also know that $A+B+C=180$. But I am unable to show it. Please help. What would I do if I want to have a generic method that only accepts types that have overloaded an operator, for instance the subtraction operator. I tried using an interface as a constraint but interfaces can't have operator overloading.   What is the best way to achieve this? Modulus with a negative number Unity remove logo in splash screen What is Interface method in salesforce Trying to wrap my head around the ways to properly handle collision in a game designed around components.  I see many examples have some sort of PhysicsComponent that gets added to the entity's list of components but the actual implementation is confusing me.  For this to work, the PhysicsComponent would need access to the world around it. This doesn't make intuitive sense to me. Shouldn't a component be unaware of not only its container (the entity), but its container's container (the world)?  To me, it sounds like the level or scene should maintain a list of these entities and every game update, loop through the entities to determine which collide.  My question is firstly, whether or not this is good design, and secondly, how to determine which entities can collide. I suppose solid entities could implement an empty IRigidBody interface so the level could determine which entities in the list support collision. But is this breaking the component design?  Instead, should they contain an empty RigidBody component? This may actually be better because it may not always be empty and this approach is more future-proof. The only problem with this is the complexity. The scene would have to loop through not only every entity, but also every entity's components to determine if it had this RigidBody component.  Thirdly, when they do collide both entities should be informed somehow and I am unsure on how to accomplish this either.  Let's say that both entities contained a HealthComponent and when they collided both their healths would be decreased by some arbitrary value, 5. I suppose it would be the scene's responsibility to handle this when it detects a collision between two entities?  But then is the scene responsible for too much? I could see this possibly getting out of hand and becoming unwieldy when the scene is responsible for many things entities should not (?) have access to.  Edit: Question updated with more details. Where do the bipolar jets of black holes come from? How are they formed? And why are they so bright? When I format a drive to NTFS under Windows and plug it into the Ubuntu machine it is perfectly usable, but when I format it under Ubuntu using Disks (delete all partitions and create one single partition with NTFS) it does not show up when plugged into the Windows machine. Please note that in both cases the USB drive contains only one, primary partition formatted to NTFS, for example: /dev/sdb - the actual device /dev/sdb1 - the only, primary partition I've observed this behaviour both with a solid state USB pen-drive as well as an external USB magnetic HDD. How to (re)format a USB HDD or a stick to NTFS under Ubuntu so it is usable under Windows? I am working on a BLDC sensorless motor. I need to detect BEMF Zero-cross event. My Motor is working on 24 Volt power.  Now I need to detect the back E.M.F. As refered in .  My MCU is working on 5V. And ADC range is 0 to 5V. I need to convert the BEMF feedback signal to ADC channed in this.  As we know voltage divider rule says:   In Figure I :-- Now signal (U) which I need to feed is applied at the middle of the two resistors R1 &amp; R7. So what is the value of voltage VU ?   In Figure II :-- Sum of U,V,W  is applied at the middle of the two resistors R11 &amp; R15. So what is the value of voltage VN ?  Also, what are the roles of capacitors C1 &amp; C4?  Please can someone explain the MATH behind this ?