How to solve $z^3 + \overline z = 0$
Complex roots of $z^3 + \bar{z} = 0$
How can I prove the following?  $\gamma (t)$ is unit speed, $\dot \gamma(t) \not= 0 \Rightarrow \ddot \gamma(t)$ is perpendicular to $\gamma(t)$   I don't really see where a problem would arise when $\dot \gamma(t)=0$ would cause such a problem How do I select an object in the 3D viewport? When starring a message from the star board, it's not reflected in the main chat window I have a production server running with the following flag: -XX:+HeapDumpOnOutOfMemoryError  Last night it generated a java-38942.hprof file when our server encountered a heap error. It turns out that the developers of the system knew of the flag but no way to get any useful information from it.  Any ideas? Best way to start investing, for a young person just starting their career? I am young, just started my career, and looking to begin investing so I can make my money work for me. I'm still living like I did in college (occasional purchase on myself, but most of it goes into savings) and I would like to take the extra money and invest it.   What would you suggest are the best options for me to begin? I was considering getting a personal investor [a financial advisor] for perhaps a year or so, but I've heard that they really are not worth the money. I wanted to get the input of the great minds here. How to influence the position of float environments like figure and table in LaTeX? How to influence the position of float environments like figure and table in LaTeX?   This is a general question and should collect useful answers for all users. I hope we can use this as a reference Why have view counters been modified? I have to do proof of $(a+b)^n$ and $(a+b)^{n+1}$ with mathematical induction.  I finished the first one $(a+b)^n = a^n + na^{n-1}b+\dots+b^n$.  I however have trouble with the second one, I don't know what to start exactly. Any help/hints? How to pull data from internal memory on an unrooted phone? Yesterday, I suddenly discovered that I had lost all the user files on the internal memory of my android phone. All my photos, my music, my PDFs, audio recordings, everything. I will explain the events leading up to this in a separate paragraph below.  I have a Lava Z90 phone and I do not use an external SD card, so I must work with my phone to recover all data. I've been googling and following stuff I get from the internet(including Stack Overflow). Here's what I have done so far.   Tried using photo recovery apps available on Play Store. None of them worked. Decided to go more technical. Enabled USB Debugging and OEM Unlocking from Developer options in my phone. Then I used ADB pull command, pull /dev/block/mmcblk0 /home/data.img to try create an image of the entire internal storage so I can analyse it using PhotoRec. It says pull: not found I assumed this is because my phone isn't rooted?  I tried to root it with the KingoRoot apk but that didn't work. I have Ubuntu on my PC and there is not KingoRoot for Ubuntu. My next step would be to use Wine to run KingoRoot on my machine and try to root my phone that way.   I have the following questions:   How can I create an image, a data dump of my entire internal storage that i can later analyse for my data? Can I do it with an unrooted phone? If not, how can I root my phone with ADB? Am I going about this right? Is there a better, easier way to recover data that I should use instead?   Thank you very much.  How I lost my data  I recently uninstalled the TikTok app from my phone. Yesterday I connected my phone to my PC over mtp and found that there were certain leftover folders on the internal memory. One was a folder with Chinese name, one was a folder called ByteDance and one folder called Thumbnails. I assumed that the first two were leftovers from the TikTok app and the third was mere thumbnails. So I deleted them to save space. Nothing happened that day, except that I couldn't access any of my WhatsApp images through WhatsApp(they were still accessible through the gallery). However, when I woke up the next morning, all my data on the internal memory was gone. I still have contacts my messages and my settings, just that everything that was accessible through the file explorer has disappeared. Terminology of the sequences of promoters in relation to DNA strands I'm studying molecular biology and I'm trying to understand an experiment which shows the importance of promoters in the relative transcription level (RT). The image below comes from Rolf Knippers' book "Molekulare Genetik" (8th edition).    The legend says (among other things):     Die erste Zeile gibt die normale "Wildtyp"-Sequenz der 5'-flankierenden Region wieder.   Which, in english, means something like:     The first line repeats the normal wild-type sequence of the 5' flanking region.   The column on the right gives the relative transcription (RT) level, 1.0 being the highest possible level of transcription. As we can see, the lines where some parts of the "5' region" have been deleted give quite low RT levels, since some regions of the promoter are missing.  My questions are the following:  1) According to  and , I understand that RNA polymerase reads and uses both coding and non-coding strands in order to synthesize RNA. Therefore, how did they manage to use the sequences strands regions had been deleted to make a polymerase "read them" and perform transcription?  2) If the polymerase reads the template strand in the 3' -> 5' sense, shouldn't we talk of "ATAT box" or "TAAC box" instead of "TATA" or "CAAT" boxes? Does it mean that the "promoter" regions they are using on the graphic above are actually on the coding strand?  Thanks a lot for your help. Is there any way to get the windows cmd shell to expand wildcard paths? Occasionally, the cmd shell's inability to expand wildcard paths can really be an inconvenience. I had to pass 100 files in a directory to a program, and couldn't type *.ext. Instead, I used mingw's 'ls' to dump the list to a file, then replaced newlines with spaces, copied and pasted into cmd. Quite a nightmare.  I suspect the answer will be no, but has anyone dealt with this or come up with any way to make this easier? Why can't light escape from a classical black hole? Could someone help me prove that given a finite measure space $(X, \mathcal{M}, \sigma)$ and a measurable function $f:X\to\mathbb{R}$ in $L^\infty$ and some $L^q$, $\displaystyle\lim_{p\to\infty}\|f\|_p=\|f\|_\infty$?    I don't know where to start. Why does every server I try say it can't connect? I just re-purchased Minecraft (because my old profile stopped working so I bought it) after not playing it for a couple of months. I've added a bunch of servers, but almost every one says "can not connect."  I know its not because the server is not 1.7.2, because I checked that they'd update. It will say "server can't connect" after a long time. I don't know if its me or the servers.  My server screen looks like this (notice the one at the bottom – it's still loading!): I can't play Pokemon GO! What's wrong? How to undelete notes on iPhone "Notes" app? iPhone has a default "Notes" app which allows us to store notes. Stored notes can be deleted by hitting the "Delete Note" button:    How do we recover a note that is accidentally deleted?  Is there anyway to undo the delete? Is "National Socialism" always capitalized? So, I'm writing a paper on the rise of communism in China. At one point I write the following:     "Today, it is well known that communism is responsible for more deaths than even national socialism."   Then, Word corrects it by capitalizing "National Socialism."   Is it always meant to be capitalized? I am simply referencing the ideology, not necessarily the Third Reich. Word didn't bother to correct "communism." I suppose since there was only one instance of Nazism (on a national scale at least) it could be considered a proper noun. How can I achieve the correct garden tap orientation when threading it in? I'm installing an external tap using a wall plate like this one:    And a tap like this one:    This might be a stupid question, but if I screw the tap into the wall plate it will end up at a certain angle. I can install the wall plate with that angle and the tap will end up with the correct orientation (i.e. pointing down). But what if I want to put another tap in later that has its thread cut slightly differently? How do I prevent it ending up upside-down or whatever? Are all the threads cut exactly the same in these taps?  This seems like a stupid design. What is the significance of momentum? I just want to get an idea what  is. I know the mathematical meaning that momentum is $mv$ where $v$ is velocity. But I don't know its significance. Like I know that Acceleration is how velocity is changing with respect to time, I wanted to get feel of what momentum really is? Seeking English term for relationship between two members of extended family?