We all know the earth is rotating around its own axis. From a physics energy point of view, some thing has to provide energy for the rotation. What provides the energy to rotate?
How do the Planets and Sun get their initial rotation? Why do Venus and Mercury rotate so slowly compared to other planets?  Why does Venus rotate in a different direction to Mercury, Earth and Mars?
A photon emitted from a receding source (Doppler redshift) has less energy when detected at an observer's location. Please explain the energy loss from the perspective of energy conservation. I saw this question: .  My situation is a little different though.   My target moves, and the shooter moves.  Also, the shooter's velocity is added to the bullets' velocities, i.e. bullets fired while sliding to the right will have a greater velocity toward the right.   What I'm trying to do is to get the enemy to be able to determine where they need to shoot in order to hit the player.  Using the linked SO solution, unless the player and enemy are stationary, the velocity difference will cause a miss.  How can I prevent that?      Here is the solution presented from the stack overflow answer.  It boils down to solving a quadratic equation of the form:  a * sqr(x) + b * x + c == 0   Note that by sqr I mean square, as opposed to square root. Use the following values:  a := sqr(target.velocityX) + sqr(target.velocityY) - sqr(projectile_speed) b := 2 * (target.velocityX * (target.startX - cannon.X)       + target.velocityY * (target.startY - cannon.Y)) c := sqr(target.startX - cannon.X) + sqr(target.startY - cannon.Y)   Now we can look at the discriminant to determine if we have a possible solution.  disc := sqr(b) - 4 * a * c   If the discriminant is less than 0, forget about hitting your target -- your projectile can never get there in time. Otherwise, look at two candidate solutions:  t1 := (-b + sqrt(disc)) / (2 * a) t2 := (-b - sqrt(disc)) / (2 * a)   Note that if disc == 0 then t1 and t2 are equal. I don't know how to solve $7^x-3^y=4$... I tried to see something $\pmod 7$ and $\pmod 3$ but it doesn't help at all. Can anyone give me some hints about it? Where are packages stored installed with APT in Ubuntu 16.04? I am new to TeX/LaTeX. How do I install TeX on Windows (7)? It seems that there are many different implementations, so which one is best for my OS? Delete votes from users who later become moderators shouldn't prevent community undeletion $\lim_{x \to 0} f(x)=\frac{\tan 3x}{\tan 2x}$ without L'Hospital Ralink MT7601U (148f:7601) Wi-Fi adapter installation I am trying to install a Ralink wifi adapter in Ubuntu Desktop 14.04.  The system is not detecting the wifi.   lsusb lists the device as:  Bus 002 Device 004: ID 148f:7601 Ralink Technology, Corp.  I have the rt2800 USB driver listed in "/etc/modules"; Following some instructions on the web, I tried this command:  echo 148F 7601 | sudo tee /sys/bus/usb/drivers/rt2800usb/new_i  lsmod | grep rt2800 returns the following:  rt2800usb              26581  0  rt2x00usb              20041  1 rt2800usb rt2800lib              83150  1 rt2800usb rt2x00lib              48886  3 rt2x00usb,rt2800lib,rt2800usb mac80211              545990  3 rt2x00lib,rt2x00usb,rt2800lib crc_ccitt              12627  1 rt2800lib Unity: How do I revert Alt-tab behavior to switch between windows on the current workspace? Enabling Bias alt-tab sorting to prefer windows on the current viewport as described  made no difference. How can I get back the exact same behavior as 11.04, so that alt-tab only switches between windows on the current workspace?  Simply disabling the alt-tab and shift-alt-tab keybindings on the unity switcher seems to have helped, but it still switches workspaces on me sometimes.  For example, if I give a terminal window focus then press alt-tab, it switches to another terminal window on any workspace before trying to switch on the same workspace. Also, the Unity switcher still shows up when I alt-tab then hold alt even though I removed its alt-tab keybinding. How to calculate stays against 90/180 visa rules? Some destinations have a "90/180 rule" which says you can come and go but you must not spend over 90 days out of any 180 days in the area.  concerns this rule.  At least Schengen and Turkey have this rule, probably depending on where the traveller is from and what kind of visa they apply for.  Maybe I'm a dummy but I've always had a lot of trouble trying to add up how many days I've spent in such places when I've entered and left several times over recent months.  Is there an easy way to do this I'm missing or is it difficult for everybody? I'm guessing something based on counting backwards from the end date might be the trick?  Maybe you know of an app or website that can do this for you. How to stop apt from doing anything Started new job. Rollover previous employer 401k to new 401k, IRA or Roth IRA? I recently started a new job and have a 401k from my previous employer that I don't know what to do with.  Should I roll it into my new employer's 401k, a traditional IRA or a Roth IRA? CPU clock speed versus CPU core count - higher GHz, or more cores for SQL Server? We are beginning to provision a set of physical servers for a virtual cluster of SQL Server 2016 nodes within VMware. We will be utilizing Enterprise Edition licenses.  We plan on setting up 6 nodes, but there is a bit of a debate on what the ideal way to provision the physical servers with regards to CPU clock speed versus CPU core count.  I know this is largely dependent on transaction volume and number of databases stored among other software-specific factors, but is there a general rule of thumb that is advised?  For instance, is a dual 8-core, 3.2 GHz physical server (16 cores) more preferential to a dual 16-core, 2.6 GHz server (32 cores)?  Has anyone come across a white paper that further delves into this type of topic? I am considering buying my first DSLR.  How do I know whether I need a 18-200 lens, 17-85, or 18-55? Or something else? After the performance problems we have run into with  we've decided to make a change, we're moving the network on to .  Here's where to get started:   What works:   All search operators should be in Many changes below from the old search behavior   What's different:   The new search is AND, adding a search term will narrow your results, not expand them. The look of search results is now more unified with the following differences between Q&amp;A:   "Q:" or "A:" prefix Answer counts and tags will be present in questions. The answer count will be highlighted in green if it's accepted. (We may index other things later, that's why the results are more generic/google-y now.)  It's faster, about 5-10x faster for almost all searches on large sites like Stack&nbsp;Overflow Quoted phrases are exact matches except for case-sensitivity, for example,  or . If not in a quoted phrase, words will now be stemmed () Snippets for context will now be more relevant Excludes are now explicitly supported (like -term and -"my phrase") We don't roll up to the question anymore, if you searched for something that matched an answer, we'll show you the answer directly in search results The search per minute limit is effectively gone, it'll block a bot, but no one else should hit it... We'll be monitoring performance though infavorites:mine is back, with infavorites:12345 (any user id) added   What needs work:   What you tell us is broken... Do your worst.   Testing, not yet final:   New range support, here are some examples:   answers:1..1 (exactly one answer) answers:10..20 (10 to 20 answers) created:2008..2009 (created between Jan 1st, 2008 and Dec 31, 2009) created:2010-04..2010-05 (created between April 1st, 2010 and May 31st, 2010) created:2011-01-05..2011-01-06 (to be clear: it goes to end-of-day) This range syntax applies to a new advanced operator: lastactive: and the other numerical ranges, views:, and score:  Additionally, the above syntax is a bit more flexible if you forget it exactly (e.g. score:20-30) in an effort to be intuitive as possible, give it a try - tell us what you think.    I'll try and improve the search as much as possible before it becomes default... At the very least we want it equivalent in relevance and functionality before the switch, but ideally much better. We won't switch until then.  Please give it a try, tell us what you think here, and we'll continually improve it over the holidays as time allows. Bear in mind you may get a search offline page during this test if a change we're making for results necessitates a reindex, and even that should only last about two minutes here on Meta&nbsp;Stack&nbsp;Overflow.  Give it your worst, compare results to the old search, tell us what's better and what's not. We look forward to the feedback.  Update The new search is now the default across the network - we'll be monitoring things over the next few days and would appreciate reports of any crazy behavior you see here. I am looking for a preferably introductory text on Yang-Mills theory with mathematical basis and language. (Differential forms) I have a background in QCD and QED, however, I want to go more in details in geometrical interpretations of Yang-Mills theory. I am sorry if this question has asked before. Thanks in advance. What can be said about the convergence on $|z|=1$? I already found the radius of convergence of the power series $:$ $$\sum_{n=1}^{\infty} \frac {(-1)^n} {n} z^{n(n+1)}.$$ What happens at the boundary of disk of convergence?  I found that the radius of convergence to be $1$ and hence the disk of convergence is $|z|&lt;1$. Now I found at $z=1$ the series converges. Now how can I proceed? Please help me. Thank you in advance. Design Review: 3.3V Logic to 12V Logic (Uni-directional and Bi-directional) I'm looking for feedback and improvements on my design below. Specific questions are at the end. I created this as an attempt to answer my own, . From my feedback there, it seems like I needed to be more clear in my requirements. These are screenshots from Eagle. If there's a better way to share, please let me know so I can correct it. Entire board  The overall purpose of this board is to translate between 12V logic, and 3.3V logic. The top portion of the board represents the 12V side. The LEDs are placeholders to indicate whether the 12V signal is HIGH or LOW. In practice, these would be replaced with more , requiring up to 3A. The switches are also placeholders, allowing one to manually turn the 12V signal on and off. They are only for test purposes, the &quot;real&quot; 12V signal would be coming as the output from other relays. The bottom half is the 3.3V side. This will be connected to a  (BBB). The board will connect to 2 output GPIO pins and 2 input GPIO pins of the BBB. Overall, I want to translate the 3.3V I/O from the BBB to the 12V signals on the other side (to control more relays and read their signals). I have designed 3 modules to control both directions individually, and together. 3V3_TO_12V Module  This module converts the 3.3V GPIO output from the BBB to a 12V signal on the other side. When the 3.3V signal is low, the 12V signal is low. When the 3.3V signal is high, the 12V signal is high. To do this, the 3.3V GPIO output is connect to a , which turns a  relay on and off. This switches the 12V power as output of the module to be used elsewhere. 12V_TO_3V3 Module  This module converts a 12V signal to 3.3V signal, to be read by a GPIO input from the BBB on the other side. When the 12V signal is low, the 3.3V signal is low. When the 12V signal is high, the 3.3V signal is high. To do this, the 12V signal simply turns a  relay on and off. This switches the 3.3V power to be read as input by the BBB. DUAL_12V↔3V3 Module  This module combines the previous two modules to create a bidirectional translation. If the 12V side is high, the 3.3V input to the BBB GPIO should be high. If the 3.3V output from the BBB GPIO is high, then the 12V side should be high too. It's similar to a logical OR, if either side is high, the corresponding signal on the other side should be high too. A single 12V signal has to be split into individual input and output signals on the 3.3V side for the BBB. Questions  Is the  and  relay combination overkill for having the BBB GPIO output control the 12V power line? I like the isolation and safety it provides, but it seems too much (in terms of cost and board space) Is there a better solution for the 12V to 3.3V conversion. I like the simplicity of the  relay switching a 3.3V signal, but it takes up lots of room. Does the DUAL_12V↔3V3 Module (which combines each translation direction) even make sense? This seems wasteful to use 2 relays and a high side driver, but I haven't found simpler solution that achieves the same result. Should I add pulldown resistors for the BBB GPIO inputs, or are the internal pulldown resistors good enough?  Any other feedback is welcome. I'm new to electronic design. How many fixed points in a permutation I am taking a probability course and we have been of course learning the classic problems of men with hats or variations of that in some other form. The problems being of the type if $n$ men have $n$ hats and mix them all together, whats the probability $0, 1, 2,$ or $k$ men choose their hat.   But from what I can gather is that they are all problems of the same type, for any given random permutation of $k$ objects how many fixed points are there. My professor taught us to solve this using conditional probabilities (conditioning on whether the first person matched and then generating a system of equations) and using the inclusion-exclusion principle. But is there any other way to reason this? Is there a rule in British English about how to pronounce "either"?